Timeline

Their relationship
-Pilot
Liz goes out with Kyle. But after the shooting and healing, she discovers that Max has feelings for her and finds her 'beautiful'. When she asks him why he risks everything to save her, he answers because 'it was you'. At the end of the episode, they talk and Max says that he truly wants things differently but they are not.

-Leaving Normal
After Liz finds out that one of Kyle's friends beats up Max for approching her, she breaks up with him. She then, finds confort in Max's arms learning the death of her grandmother who last advice was to 'follow your heart'.

-Heat Wave
The whole town is subject at a heat wave; love and romance are in the air. At the soap factory's party, Max tries to kiss Liz but is interrupted by Kyle and the police.

-The Balance
Max and Liz finally go at their first date, but Michael being sick, they have to leave and take Michael to the Indian reservation. At the end, Max decides to take a 'step back' from Liz.

-Blind date
Liz wins a contest which consist of going out on Saint Valentine day with her dream date. Max is getting drunk by Kyle, and because he has never experimented any alcohol before, it makes him reveal his true feelings to Liz: that she is his dream girl and that he loves her. But after they share a passionate kiss in front of most of the school, he realizes what he did, and leaves her, forgetting what he said before.

-Sexual Healing
Max and Liz admit their feelings toward each other, and they share a telephatic connection when they kissed. They end up finding a mysterious stone from Max's planet.

-Tess, Lies and Videotapes
Max has an uncontrollable attraction for the new girl, Tess. Liz is getting jalous.

-Destiny (season finale )
After being kidnapped by the FBI and saved, Max tells Liz that he loves her and that she is his destiny. At the cave where the pods were, the four aliens and Liz discover Max and Isabel's mother message and their destiny. Max is supposed to be with Tess. Hearing it, Liz runs down the cliff after telling Max that now he knows his destiny, she cannot stay in the way of it.

-Skins and Bones
Liz has been in Florida all summer and Max had stayed in Roswell mourning about Liz to Maria. He met her in the street surprised that she came back. They discussed and at the end of the episode, Max asked her if they could go back to the time where they were together, and she got a flashes of their moments spent together.

-Ask Not
They look in Congresswoman Whitaker's files together and at the end Max tells Liz that he does not care about his destiny but her, and that's he is coming for her.

-End of the World
Max from the future comes to see Liz and tells her that she has to help him make 'present Max' fall out of love with her. Unsuccessful first, Liz then pretends to sleep with Kyle in front of Max's eyes that leaves ravaged by what he has seen. Liz and future Max share their 'wedding dance' and he disappears leaving Liz alone.