Season 3

Penny throws herself at Leonard after he returns from three months at the North Pole where he was assisting Sheldon to look for data to prove string theory, and they begin a relationship that lasts most of the season. Penny and Sheldon start a quirky friendship (though she can still annoy him).Will Wheaton firsts appearance is in "The Creepy Candy Coating Corollary" and becomes Sheldon's arch-enemy. Howard is setup with Penney''s friend Bernadette Rostenkowski and  begins to date to date her .At the end of the season Howard and Raj put Sheldon on online dating websites, where Sheldon meets Dr Amy Farrah Fowler.

Season 2

Season two begins to deal with character development, including Sheldon becoming more and more obsessive. Leonard and Penny's relationship takes a turn for the worse when they break up, but this is quickly resolved. Soon their relationship progresses into a stronger friendship than before, while Sheldon and Penny's friendship slowly begins. In the season finale Penny hints at her true feelings for Leonard. 

 Howard  remains similar to what he was in season one in his attempts to seduce women, managing to start a short-lived relationship with fellow colleague Leslie Winkle in the second half of the season. Meanwhile, Raj manages to briefly apologize to Penny for what he did in "The Griffin Equivalency" as he was very arrogant with having consumed alcohol. Barry Kripke  makes his first appearance In the series starting with this season, He first appears in "The Killer Robot Instability".

Season 1 Overview

The first season of the Big Bang Theory is about Caltech scientists Dr. Sheldon Cooper and Dr.Leonard Hofstadter lives being spun around when an attractive avid actress called Penney moves into the apartment across from theirs.Leonard starts to fall for Penney's beauty while she wants to just be friends, as a result of this she has to put up with Leonard's roommate and closest friends Sheldon who has an eidetic memory and appears uncontrollable; engineer Howard Wolowitz a mamas boy and appearance seems like he's from the '60s; and Dr. Rajesh Koothrappali who they refer to as Raj he cannot talk to Penney or any women as he has a case of selective mutism, he can only talk to women when he is drunk.
Throughout the season Sheldon is fired because of insulting his new boss and is determined to state his dominance in the group. Raj finds out that he can finally talk to women but has to be drunk. At the end of the season Leonard and Penney go out on a date.