The story of Vishvamitra is narrated in the Balakanda of Valmiki Ramayana[1]. The Mahabharata adds that Vishvamitra's relationship with Menaka resulted in a daughter, Shakuntala whose story is narrated in the Adi Parva of the Mahabharata.

Vishvamitra was a king in ancient India, also called Kaushika ("the descendant of Kusha"). He was a valiant warrior and the great-grandson of a great king named Kusha. The Valmiki Ramayana, prose 51 of Bala Kanda, starts the legend of Vishvamitra thus, "There was a king named Kusha (not to be confused with Kusha, son of Rama), a brainchild of Prajapati, and Kusha's son was the powerful and verily righteous Kushanaabha. One who is highly renowned by the name Gaadhi was the son of Kushanaabha, and Gaadhi's son is this great-saint of great resplendence, Vishvamitra. Vishvamitra ruled the earth, and this great-resplendent king ruled the kingdom for many thousands of years.

His story also appears in various Puranas, however they show variations from the Ramayana. The Vishnu Purana and Harivamsha chapter 27 (dynasty of Amaavasu) of Mahabharatha narrates the birth of Vishwamitra. According to Vishnu Purana[2], kushika married a damsel belonging to Puru-kutsa (later called as Shatamarshana lineage - descendents of Ikshvaku king Trasadasyu) dynasty and had a son by name Gadhi who had a daughter named Satyavati(not to be confused with Satyavati of Mahabharata).

Satyavati was married to an old Brahman known as Richika who was foremost among the race of Bhrigu. Richika desired a son having the qualities of a Brahman, and so he gave Satyavati a sacrificial offering (charu) which he had prepared to achieve this objective. He also gave Satyavati's mother another charu to make her conceive a son with the character of a Kshatriya at her request. But Satyavati's mother privately asked Satyavati to exchange her charu with her. This resulted in Satyavati's mother giving birth to Vishvamitra, the son of a Kshatriya Gadhi with the qualities of a Brahman; and Satyavati gave birth to Jamadagni, the father of Parasurama, a Brahman with qualities of a Kshatriya.
On one of his exploits, he and his soldiers took rest in the ashram of Rishi Vasishta. There, his whole army was well fed and taken care of. This caused a doubt in the king's mind as to how it was possible for this simple ashram to take care of all the arrangements to feed an entire army. He expressed his surprise to the sage. Vasishta replied,

"O king, this feast that you have partaken with your kinsmen, has been provided by my calf Nandini (sometimes referred as Sabala), who was gifted to me by Indra. You must know that she is the daughter of Indra's cow Kamadhenu. She provides me with everything I need."

Kaushika was filled with wonder when he heard this. He began to think that possessing this cow would mean a lot to him; after all, the sage did not have to provide food and sustenance for a large army everyday. He expressed a desire to the sage for obtaining Nandini from him. Vasishta was polite, but steadfast in his refusal. He would not be tempted by the offer of untold wealth that was made by Kaushika, for after all who can set a price on a cow, which can readily yield all the riches in the world.

The king grew exceedingly angry. He insulted the Brahmarishi with harsh words, and ordered his soldiers to seize the cow, and drive it to his kingdom. By his yogic powers, the great sage Vasishta, called forth an entire army of fierce warriors. They fought the army of Kaushika and defeated it thoroughly. Kaushika was captured and presented before Vasishta. The sage pardoned the king and sent him away with words of advice.
In other version, Vasishta destroys Kaushika's entire army by the simple use of his great mystic and spiritual powers, breathing the Aum syllable. Vasishta also thus kills one hundred of Kaushika's sons, while restoring his hermitage's beauty and life.

Kaushika then undertakes a tapasya for several years to please Lord Shiva, who bestows upon him the knowledge of celestial weaponry. He proudly goes to Vasishta's ashram again, and uses all kinds of powerful weapons to destroy Vasishta and his hermitage. He succeeds in the latter but not in the former.

An enraged Vasishta brings out his brahmadanda, a wooden stick imbued with the power of Lord Creator Brahma. It consumes Kaushika's most powerful weapons, including the brahmastra. Vasishta then attempts to attack Kaushika, but his anger is allayed by the Devas. Kaushika is left humiliated while Vasishta restores his hermitage.
This incident made a deep impression on the King. He realized that the power obtained by penances was far greater than mere physical might. He renounced his kingdom and began his quest to become a greater rishi than Vasishta. He took on the name Vishvamitra. It is very interesting to see all the challenges that Visvamitra faced in his life to become a Brahmarishi, before eventually giving up the greed to possess the cow. After many trials and undergoing many austerities, Vishvamitra at last obtained the title of Brahmarishi from Vasishta himself. During this time he had a daughter named Shakuntala (who appears in the Mahabharata) with Menaka, an apsara in the court of Indra. Son of Shakuntala became a great emperor. He came to be known as Emperor Bharata and it is in his name that the land of India got its name Bharat.
Kaushika seeks to attain the same spiritual power as Vasishta, to become his equal, a brahmarishi. He undertakes a fierce penance for one thousand years, after which Brahma names him a Rajarishi, or royal sage.

After another long penance of ten thousand years, Brahma names him a rishi, thus leaving his royal lineage permanently.

At this point, Indra, the king of Swarga attempts to test the tapasvin by sending Menaka, an apsara to seduce him. Kaushik then lives with Menaka for 10 years. They have a baby girl Shakuntala. Kaushik becomes angry as Menaka had destroyed his years of meditation and thus he cursed her that she won't possess her beauty, of which she was proud, in next birth. And hence in the next birth she became a monkey and mother of Hanuman, Anjani.

Kaushika now goes to the banks of the river Kaushiki, which is the spirit of his own sister. After many thousands of years of penance, Brahma names him maharishi, but also tells him that he hasn't become a jitendriya yet, lacking control over his passions. This is brought to light to Kaushika when he angrily curses Rambha, an apsara sent by Indra to seduce Kaushika again, to become a stone for a thousand years.
After cursing Rambha, Kaushika goes to the highest mountain of the Himalayas to perform an even more severe tapasya for over a thousand years. He ceases to eat, and reduces his breathing to a bare minimum.

He is tested again by Indra, who comes as a poor Brahmin begging for food just as Kaushika is ready to break a fast of many years by eating some rice. Kaushika instantly gives his food away to Indra and resumes his meditation. Kaushika also finally masters his passions, refusing to be provoked by any of Indra's testing and seductive interferences.

At the penultimate culmination of a multi-thousand year journey, Kaushika's yogic power is at a peak. At this point, Lord Brahma, at the head of the Devas led by Indra, names Kaushika a brahmarishi, and names him Vishvamitra, or Friend of All for his unlimited compassion. He is also embraced by Vasishta, and their enmity is instantly ended.
As a former king, and one over as vast a realm as he had been, Vishvamitra was known to retain a regal and often haughty bearing. He was known for his high temper and often cursed people in his anger, thereby depleting his yogic powers obtained by much penance. People feared his temper and prayed that their actions might not get misconstrued by the touchy sage.

However, as a former king, Vishvamitra also possessed great compassion for all beings. Having taken pity on Trishanku, he willingly exhausted all the punya he gained from his tapas, to enable him to ascend to the heavens. Following his attainment of the status of brahmarishi, he was known to use the power of his tapas to help anyone who was in need, whatever the cost to himself.

Kaushika's love of Menaka is considered to have been intense and passionate beyond estimation.
Vishwamitra was the author of the revered great Mantra - The Gayatri Mantra. It is a mantra come prayer and is found in all the three Vedas; Rig, Yajur and Sama Veda. Vedas clearly state that anyone can chant this Mantra, and gain its benefits. Gayatri Mantra:

Om Bhur Bhuva Svah,
Tat Savitur Varenyam.
Bhargo Devasya Dhimahi
Dhiyo yo nah prachodayat

Meaning:

We meditate on the glory of the Creator;
Who is worthy of Worship,
Who is the source of knowledge,
Who is the bright light,
May he illuminate our intellect.

Gayatri Mantra is so called because it liberates one who chants it.
Another story Vishvamitra is known for is his creation of his own version of Svarga or heaven, called Trisanku Svarga. When a proud King Trisanku asked his guru, Vasishta, to send him to heaven in his own body, the guru responded that the body cannot ascend to heaven.

King Trisanku then asked Vasishta's hundred sons to send him to heaven. The sons, outraged that Trisanku should not come to them when their father had refused, cursed him to be a Chandala, or untouchable. Trisanku was transformed into a person with body smeared of ash, clothed in black and wearing Iron jewellery. Since none of his subjects could recognize him, he was driven out of the kingdom.

He came across the sage Visvamitra, who agreed to help him. Visvamitra organized a great sacrifice and ritual proptiating the Devas, pleading that they accept Trisanku in heaven. Not one Deva responded. Angered, Visvamitra used his yogic powers and ordered Trisanku to rise to heaven. Miraculously, Trisanku rose into the sky until he reached heaven, where he was pushed back down by Indra.

Enraged even more by this, the powerful Visvamitra then commenced the creation of another heaven for Trisanku. He had only completed the heaven when Brihaspati ordered him to stop. Trisanku, however, did not enjoy Trisanku Svarga, he remained fixed in the sky and was transformed into a constellation.

In the process of forming a new universe, Vishvamitra used up all the tapas he had gained from his austerities. Therefore after the Trisanku episode, Vishvamitra had to start his prayers again to attain the status of a Brahma Rishi, to equal Vashistha.
While undertaking a penance, Kaushika helps a boy named Shunashepa who has been sold by his parents to be sacrificed at Harishchandra's yagna to please Varuna, the God of the Oceans. The king's son Rohit does not want to be the one sacrificed, as was originally promised to Varuna, so young Sunashep is being taken. A devastated and terrified Sunashepa falls at the feet of Kaushika, who is deep in meditation, and begs for his help.

Kaushika teaches secret mantras to Sunashepa. The boy sings these mantras at the ceremony, and is blessed by Indra and Varuna, and Harishchandra's ceremony is also completed.
In the Indian epic Ramayana, Vishvamitra is the preceptor of Rama, prince of Ayodhya and the seventh Avatara of Vishnu, and his brother Lakshmana.

Vishwamitra gives them the knowledge of the Devastras or celestial weaponry [ bala and adi bala ], trains them in advanced religion and guides them to kill powerful demons like Tataka, Maricha and Subahu. He also leads them to the svayamvara ceremony for princess Sita, who becomes the wife of Rama.
People belonging to the Visvamitra Gotra consider Brahmarishi Visvamitra as their ancestor.

There is an off-shoot of "Vishvamitra Gotra" called "Chakita Vishvamitra Gotra". Two explanations have been suggested for this off-shoot. The group is supposed to have sprung from a "surprised" reaction of Vishvamitra. The other, more likely, explanation, is that a group of descendants decided to split from the main group and started their own branch of this line.
People belonging to Kaushika ( Kaushik /Kousika/Kousikasa/Koushika/Kausika) Gotra take Rajarishi Kausika as their root. Kausika was one of the names of Visvamitra.11 Royal clans of 96 clan of Marathas belong to Kaushik gotra including the illustrious house of Shivaji and Rashtrakutas. 2 more clans belong to the Vishvamitra gotra. Kaushika gotra also belongs to Baish clan of rajput which includes in the suryavanshi rajput.Many Kashmiri pandits belong to Kaushika gotra.Many Kanyakubji bramhins found in different states also belong to this gotra ,as their forefathers have migrated from kashmir valley before settling around Kanyakubja (present day Kanauj in U.P.India). Many Deshastha and Kokanastha Brahmins from Indian State of Maharashtra belong to Kaushik Gotra.