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Here are the recaps for each of the 17 episodes for Season One of The Big Bang Theory.
E1: Pilot
Here we first meet our socially awkward genius protagonists Leonard and Sheldon and their perky new neighbor Penny. Leonard is immediately attracted to Penny and invites her into their lives so that they will never be the same. Leonard also volunteers himself and Sheldon to retrieve Penny's TV from her gigantic ex-boyfriend. We also meet the final two members of their geek-squad, Howard and Raj.
The pilot, like most, does not quite have all the characters down and introduces a few elements that are disregarded in the rest of the series such as Sheldon being attracted to Penny.
E2: The Big Bran Hypothesis
After being entrusted to put a delivery of furniture in Penny's apartment, Sheldon and Leonard see the interior of Penny's apartment. Sheldon is traumatized by the chaos and messiness. Because of this, Sheldon uses the spare key to sneak into Penny's apartment while she is asleep to tidy up and organize her things. He ropes Leonard into his craziness and they both participate. The next day when Penny wakes up, she is livid that they broke in to her apartment. She does forgive them shortly after once realizing that they didn't mean any harm and are actually nice guys.
E3: The Fuzzy Boots Corollary
Jealous of Penny's date, Leonard decides to go on one of his own. He starts by asking Leslie Winkle, a collegue of his, who turns him down after an unexciting kiss. Annoyed by Leonard's moping after this embarrasing episode, Sheldon points out that Leonard never asked Penny out, which he proceeds to do. Penny misunderstands however, thinking it's going to be everyone hanging out. After a sweaty panic attack, Leonard takes her out to dinner with elaborate excuses for where the other guys are. He also manages to split his head open and throw up in Penny's car. Once home, Penny asks if that was supposed to be a date and Leonard denies it.
E4: The Luminous Fish Effect
After insulting his new boss, Sheldon gets fired. Sheldon looks at this as an opportunity to start experimenting with everything he's ever wanted to, starting with eggs, weaving, and luminescent fish. It also includes a failed shopping trip with Penny, his idea for a bulk mail order feminine hygiene business, and an obsession with ponchos. Desperate, Leonard calls Sheldon's pleasant and very religious mother to talk some sense in him. She ends up coercing him into apologizing to Gablehouser and gets his job back while flirting with his boss.
E5: The Hamburger Postulate
After a kiss that didn't make the world spin, Leslie Winkle has a change of heart and seduces Leonard into a sexual relationshipwith some seductive string music and literal sweet talk. Everyone else becomes aware of this when Sheldon brings Penny to inspect and explain the sock on Leonard's doorknob. Then Leonard gets suspicious of whether Penny is jealous or not. However, Leonard was under the impression that his night with Leslie would lead to more before being corrected in no uncertain terms by Leslie herself.
E6: The Middle Earth Paradigm
Penny throws a Halloween party and the guys are invited. Of course, despite the great joy they take in dressing up in costumes, its subdued somewhat by the fact that they are incapable of really mingling with people. It's also exacerbated for Leonard by Penny's ex-boyfriend showing up to embarass him. A distraught and drunk Penny comes to check on Leonard. She's confused and ends up crying and kissing him. He comforts her and sends her home.
E7: The Dumpling Paradox
Penny's friend invites herself to stay at Penny's apartment. So while Penny is hiding in Leonard and Sheldon's apartment, Howard makes his move on Christie, the unfriend slutbag, and lands himself a girlfriend by spending his pants off on her. Rather than listen to Howard make girly moans in her apartment, she instead kicks ass at Halo night then sleeps on their couch. She relocates to live with Howard who spends all his free time with her. Sheldon wreaks havoc once his routine is disturbed and goes to beg Howard back. Christine ends up walking out after a fight with Howard's mom, effectively getting Sheldon his fourth back.
As a side note, in this episode Raj speaks in front of Penny. As he was not facing her at the time it's possible that he was unaware that she was in the room, though he usually reacts more strongly when he's made aware of his error. So it's uncertain whether he didn't know or this was just a continuity error.
E8: The Grasshopper Experiment
Raj is distressed after his parents meddle in his love life, inviting a girl he knew as a child to meet him and potentially be his wife. Knowing he can't actually talk to her, Howard imitates Raj and asks her to go on a date. Meanwhile, Penny wants to practice her bartending skills and Raj enthusiastically agrees to drink due to stress. After a sip, Raj is suddenly able to speak to Penny. Realizing all it takes is some alcohol, Raj attempts his date while drinking. Of course, they weren't expecting it to make him a dick. He ruins his date with Lalita and Sheldon swoops in to accidentally steal her after he unintentionally charms her pants off. We are also introduced to drunk!Sheldon in this episode when Penny sluts up Sheldon's virgin drinks.
E9: The Cooper-Hofstadter Polarization
After Sheldon receives a letter asking him and Leonard to present their paper at a symposium, Leonard finds it in the trash. Leonard tries to convince him to go so they can present, but Sheldon remains obstinate. Leonard plans on going even though Sheldon forbids it. However, Sheldon is unable to let Leonard take the credit and glory, so he shows up to the symposium. The two end up getting into a fights that lands them on Youtube thanks to Howard.
E10: The Loobenfeld Decay
When Penny gets a part in a musical that allows her to sing (and peel the paint off walls), Leonard lies to her to get himself out of going to see her perform. Uncomfortable with Leonard's simple lie, Sheldon tells Penny a convoluted story involving Leonard protecting Sheldon's reputation because they were going to participate in a drug intervention with Sheldon's fake cousin Leo. To add more proof to the lie, Sheldon hires an actor to play Leo. Penny meets "Leo" and just believes that the guys are being good and respectable friends. She then invites Leonard over to have coffee and watch a video of her performance.
E11: The Pancake Batter Anomaly
Penny returns from a family trip to Nebraska bearing a contagious flu virus. Sheldon gets sick and Leonard along with Howard and Raj escape to a Planet of the Apes marathon to avoid a sick, clingy, and annoying Sheldon. When he shows up to The Cheesecake Factory, Penny gets roped into taking care of him until Leonard has to return for a spare pair of glasses. She passes him back off to Leonard and makes a run for it. We are also introduced to the first appearance of the "Soft Kitty" song.
E12: The Jerusalem Duality
When Leonard and Sheldon are tasked with securing a hot new teen scientist for the physics department, Sheldon gets his feathers ruffled when the young Dennis Kim challenges his intellect. Convinced that he is outmatched by Dennis, Sheldon decides to abandon his work and tries to work with each of his friends in turn, kicked out by each due to his ego. To saves themselves from crazy Sheldon, they guys scheme to knock Dennis off his pedestal. They figure a girl is the best solution. Dennis finds one without their help and spirals downward, leaving Sheldon to resume his own work.
E13: The Bat Jar Conjecture
With the best team out of the Physics Bowl this year, the four friends decide that this is their year. Sheldon is reluctant to be their fourth, but ultimately gets kicked off the team after being an ass. He decides to form his own team to challenge his three friends. Leonard's team must fill their fourth slot and choose Leslie Winkle, though there was some great and probably unintended foreshadowing when Raj mentioned how smart TV's Blossom actually is in real life. Their team ends up beating Sheldon's team after Sheldon refuses to accept the answer of his teammate.
Also, this is the second episode where Raj accidentally speaks in front of Penny.
E14: The Nerduana Annihilation
Leonard ends up being the winner of an Ebay auction and becomes the proud owner of 1/4th of the time machine from the movie The Time Machine. When it blocks Penny from getting to work on time, she yells at the boys about getting real lives and not obsessing about toys. Leonard is about to give up all his collectibles as well as his share of the time machine, but Penny apologizes about her outburst. On the verge of asking her out, Penny's new boy toy comes to her house and Leonard decides to keep the things he loves.
E15: The Pork Chop Indeterminacy
When Sheldon's hot twin sister comes into town, the boys start to lose their minds fighting over her. Raj starts taking an experimental drug that causes some side effects and they argue over who has the right to woo her. Meanwhile, Sheldon ignores them all and Penny saves Missy by whisking her away to her apartment for some girl time. Sheldon is also convinced that he should be responsible for choosing his sister's mate and get caught pimping her out for cheese. He is then violently convinced that this is a bad idea by his sister. They discover the flaw in their plan though when Missy isn't interested in the "winner" and is instead interested in Raj, whose drug wares off at an inopportune moment.
E16: The Peanut Reaction
With Leonard's birthday coming up, Penny finds out that his family doesn't celebrate them. Feeling that Leonard secretly always wanted one, she is determined to throw him a surprise party. She ends up having to take Sheldon to the store so he could buy a present and gets stuck there while Sheldon takes customers. Meanwhile, Howard has to keep Leonard out of the house so they can set up. He stages an allergic reaction to get them out of the house, but realizes that won't keep Leonard away long enough. In order for Penny to tell him which of her friends are easy, he actually eats a peanut so he will have to stay at the hospital while they treat him. Leonard and Howard end up back at the apartment nearly an hour after the party ended, but gets to watch a drunk Raj tell him how great it was.
E17: The Tangerine Factor
Penny breaks up with her boyfriend after he cheats on her and Leonard tries to comfort her. He does so but inadvertantly encourages her to apologize to her ex for overreacting instead. Penny finds him already sleeping with another woman and takes it out on Leonard. She is again distraught and ranting about being done with jerks. Leonard asks her out on a date and she agrees to go. Both Penny and Leonard are nervous and ask Sheldon to help them out. He introduces the topic of Schrodinger's cat that convinces them both. Before the date, Leonard and Penny kiss and she proclaims that the cat is alive, so they head out the door to their dinner reservation.
on Amazon. All screencaps were taken by me.