The advent of Vishwamitra and the Swayamvara

Brahmarshi Vishvamitra ("all-friend" in Sanskrit) is one of the most venerated rishis or sages of ancient times in India. He is also credited as the author of most of Mandala 3 of the Rigveda, including the Gayatri Mantra. The Puranas mention that only 24 Rishis since antiquity have understood the whole meaning of, and thus wielded the whole power of, the Gayatri Mantra. Sage Vishvamitra is supposed to be the first, and Sage Yajnavalkya the last.
This Vishvamitra who gained Brahmarshi status from that of a Rajarshi initially was a king of name Kaushika who had a quarrel with Vashishta over the possession of the divine cow Kamadhenu. He was rejected the custody due to the fact that he was a Kshatriya and not a Brahmarshi as Vashishta was. This kickstarted the desire in him to become Brahmarshi. He renounced his kingdom, progeny, and the throne, came into the wild forests of his kingdom to do intense penance. He was gradually promoted to the post of Rajarshi, but was denied Brahmarshi due to his falling for Menaka's lures and also cursing Rambha for trying to lure him.
Then after some intense penance of some multi-thousand years, he attains the post of Brahmarshi granted by Lord Brahma, and is accepted with open hands by Vashishta.
Once, he comes to Dasharatha and tells him about the problems he is facing while performing his everyday yagnas due to the Rakshasi by name, Tadaka.
Tadaka happened to be Ravana's maternal grandmother, wife of Sumali, mother of Kaikesi, Ravana's mother. She, supported by her two sons Maricha and Subahu, used to wreck havoc when the Rishi would be performing his yagnas.
He asks the king if he could send Rama and Lakshmana with him to protect the yagna from disruption. The king immediately refuses fearing the princes weren't old enough for facing demons. He says he would come and serve the rishi personally, but was not ready to send his children. The rishi would only have his way, and wasn't ready to compromise on the princes for the king. He became red with anger, and was ready to leave saying he didn't want to go with anything other than empty hands or what he intended to take with him. Then Vashishta told Dasharatha that if Vishvamitra was insisting so much, he would have some reason in him.
After lot of contemplation, and with tears in his eyes, Dasharatha sends his sons to serve Vishvamitra.
Vishvamitra starts his yagna and it proceeds without hindrances for the first few days. Then, one day Rama notices some piece of meat faliing towards the sacrificial fire. With some really quick reflexes, Rama dispatches it back to the skies. Then came Tadaka in her fierce form, with all sorts of meat, and weapons in her hand. She tried to cause havoc, but Rama formed a protective shield over the sacrificial fire.He was hesitant to kill her because she was a lady. But Vishvamitra told him that she is not a lady for she doesn't satisfy any criterion one should satisfy to be a woman. So it was absolutely right to use a weapon against Tadaka. With this insight, he shot an arrow right into Tadaka's heart. There fell the beast right into the ground making a huge noise.
On hearing this news, her sons Maricha and Subahu rushed to the spot. They tried attacking the brothers whose arrows they weren't able to answer. Then, Rama used the Vayu astra which sent Maricha injured, yojanas away. Subahu, who did not learn a lesson from this, further attacked Rama, only to be killed.
Following this, Vishvamitra was able to complete the yagna, following which, he was extremely pleased with Rama's and Lakshmana's service. So, he taught them the great principles of Bala and Adibala respectively, and imparted to them the Tharaka mantra.
Then one day, Vishvamitra recieves an invitation to attend the Swayamvara of Sita, the daughter of Janaka, the king of Mithila.
Sita was a foundling, discovered in a furrow in a ploughed field, and for that reason was regarded as a daughter of Bhudevi, the earth Goddess. She was found and adopted by Janaka, king of Mithila (modern-day Janakpur, Nepal) and his wife Sunayana. Upon her coming of age, a swayamwara was held to select a suitable husband for her.
The Siva Dhanush which had to be strung for Sita to select her husband was a bow which was presented to Janaka by Lord Siva himself. Only Sita had been able to string it before and hence, it was found to be quite a task to accomplish.
Now, Vishvamitra who knew these details, also knew that Rama had the capability to accomplish this task. So he decided to take Rama to Mithila. On the way, Rama was asked by the Brahmarshi to step on one particular stone. When stepped on, came a beautiful woman. She introduced herself as Ahalya, the wife of sage Gautama.
Ahalya was the beautiful wife of Sage Gautama. Indra, on one of his trips to the earth, saw her and lusted for her. So when Gautama had gone to have a bath, he came to his ashram in the guise of Gautama. He satisfied his sexual needs with Ahalya in the form of Gautama, and before he could escape, the noble Gautama was back. The sage whose tapas had given him immense powers could see through Indra's guise. He cursed Indra with constant doom from demons and his wife to become a stone forever. But then, he realised his wife wasn't to blame and she was chaste indeed. So he modified the curse, saying that she would be redeemed once Lord Vishnu in human form places his divine feet on the stone.
Now, when Rama placed his foot on the stone, Ahalya was redeemed. After her salutations, Vishvamitra proceeded with Rama and Lakshmana.
They entered Mithila city, where the people on their entry rooted for Rama to be the city's new son-in-law.
The swayamvara began, where big kings including Ravana, were unable to do anything about the bow. It couldn't be strung by anyone.
In came Rama. Sita was hoping in her heart of hearts for Rama to string it. Rama bent the bow, strung it and then broke it with a thundering noise, which broke the doubts of Rama being Janaka's son-in-law in everyone's hearts.
Janaki was his. Dasharatha was called to Mithila, and Lakshmana's wedding was arranged with Sita's sister Urmila.
Then Kushadhwaja, younger brother of Janaka, comes to Janaka with a proposal asking if he could marry off his daughters Mandavi and Shruthikirthi to Bharatha and Shatrughna respectively.
When both parties were fine with the marriages, the four marriages happened with much pomp and glory.
After that, when the groom's party were returning to Ayodhya, sage ParasuRama, an incarnation of Lord Vishnu himself,and a hater of Kshatriyas, approached Rama asking him to break the Vishnu Dhanush if he could. Rama does it with considerable ease and hence makes ParasuRama realise that he himself is the Supreme Soul incarnate. With this, ParasuRama decides to leave the Dharma in the world to be established by Rama, and retires to do tapas.
Following this, Rama lives happily with Sita for plenty of years, where they live the life of a righteous husband-wife flawless for many years.