Baal Kaand

In the Balkand, Valmiki’s Ramayan starts with two brothers who are roaming around in the streets of Ayodhya. They are singing Sita’s song. It is essentially the Ramayan, but they call it by Sita’s name. Shri Raam calls them in and makes them recite the song in front of Him. The city of Ayodhya is described. It is ruled by Dashrath, who has three wives. They don’t have sons so he calls his son-in-law and performs a putrakameshthi yadnya and finally gets 4 sons. When Raam becomes old enough, Vishwamitra takes Him away, with Lakshman, to kill demons who are wrecking havoc in the beautiful jungle where rishis meditate. Raam kills some demons, (Marich escapes) and then gets married to Sita. Side by side, Dashrath is called, and Lakshman, Bharat and Shatrughna also get married.

Ayodhya Kaand

When Bharat and Shatrughna have gone to Rajgriha to meet their maternal uncle, Manthara influences Kaikeyi who forces Dashrath to throw Raam out into the jungle for 14 years and make Bharat king. She hopes that in that time, Bharat will make his name amongst the general people and they will accept him as their king over Raam. Raam leaves. Sita and Lakshman go with Him. Dashrath has something like a heart attack. Dashrath dies. The people of Ayodhya follow Raam, but He manages to lose them.

Bharat and Shatrughna naturally have a fit when they come back and learn of this. Bharat then gives orders to construct a highway all the way into the jungle to bring Raam back. After some confusion, during which some people think Bharat is trying to kill Raam, Bharat returns to Ayodhya with Raam’s sandals. He places these on the throne and rules as regent (guardian).

Aranya Kaand

Jatayu meets them in the forest and introduces himself as a friend of Dashrath. Shurpanakha flirts with Raam, Lakshman, and then again with Raam and then tries to eat Sita when Lakshman cuts her ears and nose off. She complains to Khar and Dushan who come with their armies. The entire army as well as the rakshas themselves get killed by Raam alone. Shurpanakha then tells all this to Ravan and also tells him that Sita is very beautiful. Ravan goes to kidnap Sita and with the help of his maternal uncle Marich (who is forced to become a part of this plan), kidnaps Her while the two Raghus are away.

Jatayu, a vulture, sees Ravan and tries to stop him, but is killed by the rakshas. Raam and Lakshman meet a series of people who lead them to Sugreev of Kishkindha.

Kishkindha Kaand

Raam and Lakshman meet Hanuman for the first time who introduces them to Sugreev, the king-in-exile. He has a disagreement with Vali because the latter maintains that Sugreev usurped his kingdom.

Once Vali went under the ground to fight a demon. It was agreed between Vali and Sugreev that if Vali does not return in a stipulated period of time, Sugreev is to claim the kingdom. Vali did not return and Sugreev took the kingdom. Vali returned after this and accused Sugreev of being an usurper and chased him around the world.

Sugreev agrees to help Raam but he is powerless without his kingdom. Therefore Raam kills Vali and Sugreev gets his kingdom and authority. He calls all the monkeys in the world and calls for a search from Indonesia in the east to Arabia in the west and from the Arctic Circle in the north to the South Pole in the south. Finally the group that has headed for the south pole meets Sampati, brother of Jatayu who tells them that Ravan lives on a golden island in the sea, called Lanka.

Sundar Kaand

Hanuman goes as a scout to Lanka and finds Sita. He gives Her the ring that Raam has given Him. Hanuman causes devastation in Lanka, is arrested and tries to put some sense into the King of Lanka. Ravan does not listen to Him and sets His tail on fire (because Hanuman comes across as a messenger, is protected by diplomatic immunity and cannot be killed). Hanuman sets Lanka on fire instead and goes back to inform His brethren of His discovery.

Yuddha Kaand

The monkeys and bears build a bridge, go to Lanka with Raam and Lakshman, and war takes place. Raam kills Ravan and makes Sita undergo agniparikshaalthough the others don’t seem to like it. He also coronates Bibhishan as the new King of Lanka. Sita undergoes agnipariksha and comes out of the fire unharmed after which Raam takes Her and goes to Ayodhya with the monkey army.

*Falashruti*

This is the most interesting part. There is a falashruti after Raam and Sita come to Ayodhya. This probably means that Valmiki finished his Ramayan here. After this, starts the Uttar Kaand which is supposed to be an interpolated text. It contains many contradictions to the other kaands but offers a backstory of Ravan and also ends the original story which is about the twins who have been singing Sita’s song.

Uttar Kaand

After being crowned king, Raam passes time happily with Sita. After some time, Sita gets pregnant. The people of Ayodhya start talking about Sita’s long stay in Ravan’s custody. Raam bows to the public and banishes Sita to the jungle, something which Lakshman is forced to oversee although he is against it. Valmiki provides shelter for Sita in his hermitage. She gives birth to twins, Luv and Kush. Valmiki composes the Ramyan and teaches it to Luv and Kush. When Raam holds the Ashwamedh Yadnya, Luv and Kush sing the Ramayan in the presence of Raam and His vast audience. Raam gets very uncomfortable. When Luv and Kush recite about Sita’s exile, Rama becomes grief-stricken and Valmiki produces Sita. Raam is a king of the people and populism dictates that She ought to prove Her purity in front of the public. Sita calls upon Earth, Her mother, to receive Her and as the ground opens, She vanishes into it. Raam then learns that Luv and Kush are His children. Many years later, a messenger from the Gods appears and informs Raam that the mission of His avatar is over. He returns to His celestial abode along with His brothers.

So you see, the actual Valmiki Ramayan ends after the Yuddha Kaand, but still leaves some questions unanswered. Answers to those questions are found in the Uttar Kaand, which is, unfortunately fraught with contradictions. Because of this, your question isn’t easy to answer. I believe parts of the Uttar Kaand to be later additions and parts that conform to the rest of the text to be authentic, written by Valmiki later as an epilogue.