"The Birth of Gillmon - The Digimon I Though Of"
(This is the pilot episode where Takato and Gillmon are introduced.)
"You're My Friend - Terriermon Appears"
(Gillmon runs loose around the school and Lee is introduced.)
"Renamon vs Gillmon - The Life of a Digimon is to Fight"
(Ruki appears and challenges Takato.)
"Trail Of The Tamers - Defeat Gorrillamon"
(A Lee-fixated episode where Terriermon digivolves.)
"Let's Play with Culumon"
Takato and Lee get to school one morning and find a crowd huddled around the schoolyard looking at mysterious white lines painted overnight. Culumon, still wandering without a partner, had been watching the kids play soccer and dreamed of doing it himself, so he'd broke into the supply closet. Takato and Gillmon find Culumon, and Takato, with Lee and Terriermon's help, decides to find Culumon's partner. Meanwhile, Culumon and Gillmon leave the hideout (I'm not sure what it is exactly), and end up breaking into the supply closet again. A fog appears and an evil Digimon inside it wants to battle! Lee and Takato show up just in time, and Lee sends Terriermon in to battle too. Just as things aren't going too well, Ruki and Renamon show up, and Renamon destroys the Digimon. Takato tries to explain to her that she just killed a living Digimon, but Ruki turns and leaves. Culumon runs off again, and the next day, the school children gawk at the remains of the battle in the schoolyard.
"The Meaning Of The Tamer - Renamon's Evolution"
(A Ruki episode where Ruki and Renamon go looking for a battle so Renamon can digivolve.)
"Gillmon's Crisis - Venture in my Town"
(Takato finally is able to talk to Ruki, but Gillmon disappears.)
"Gillmon's Evolution - The Large Decisive Battle in West Shinjuku"
(A high-stakes battle in which Gillmon digivolves to Growlmon, his champion form as drawn by Takato.)
"Returning to Gillmon - Growlmon's Disturbance"
(Gillmon has a slight problem de-digivolving. ^__^)