1: A Rat Problem - The Elder Scrolls IV: Oblivion
Speak to Azzan in the Anvil Fighters Guild hall. He should be in the Guild Hall starting at 11:00AM, and remain there until dark. Select the 'Contract' dialogue option to take on a job.
Arvena Thelas, a woman who resides in Anvil, is experiencing a rat problem. You'll have to travel to her house and speak to her to learn more. Don't let this seemingly mundane contract deter you from the Fighters Guilds; you'll be tasked with killing bigger things soon enough. Set 'A Rat Problem' as your active quest and follow the quest marker to Arvena Thelas.
Perhaps Arvena's rat problem is not quite what one would expect. Arvena keeps several rats as pets, but something has been killing them. She requests that you go down to the basement where she keeps the rats to investigate. Head down to the basement, and it becomes readily apparent what has been happening to Arvena's pet rats; a Mountain Lion has found its way inside! You have to act fast, because if the Mountain Lion is able to kill every one of the rats in the basement, Arvena will not push the contract any further.
Slay the Mountain Lion in Arvena's basement before it kills her pet rats!
Once you have dealt with the Mountain Lion in the basement, head back upstairs and share your discovery with Arvena. She'll point you towards Pinarus Inventius, a hunter who lives in Anvil. With his help, you should be able to determine if there are more mountain lions lurking about. Follow the active quest marker to Pinarus' location and speak to him about the mountain lions. He quickly agrees to help, so start following him out of the city.
You won't have to travel far before coming across the lions' den. When Pinarus comes to a stop outside the city gate, turn to your left to spot a small clearing where several mountain lions should be standing. Kill each and every Mountain Lion here, then return to Anvil and speak to Arvena to tell her of your success.
Just when you thought your work was done, it turns out that another Mountain Lion has found its way into Arvena's basement! Fantastic. Head down to the basement, kill the thing, and then speak to Arvena once more. Arvena is convinced that her neighbour, Quill-Weave, is to blame for these incidents. She insists that she has seen her outside at night, sneaking around behind her house. You'll need to observe Quill-Weave starting at around dusk to determine if she is truly the one behind this. You must not be seen, otherwise Quill-Weave is likely to become suspicious.
Wait outside Arvena's house starting at around 7:00PM, as Quill-Weave should appear at this time. The active quest marker now points to Quill-Weave, so you can keep track of her by checking the local area map. Wait in the backyard of the house next to Arvena's for Quill-Weave to appear. Remain in Sneak Mode, and out of Quill-Weave's view. When you notice her slip behind Arvena's house, keep an eye on her while still in Sneak Mode.
Wait for Quill-Weave to appear outside of Arvena's house after nightfall.
You'll witness her leaving a slab of meat outside of Arvena's house. After catching Quill-Weave leaving the meat, run up and confront her. If you agree to not tell Arvena what you saw, Quill-Weave will grant your character one Acrobatics skill level. If you do tell Arvena, she will grant your character one level of Speechcraft. Decide which skill level you would rather have your character gain, and act accordingly. If you decide to lie and tell Arvena that Quill-Weave had nothing to do with it, after receiving your payment, speak to Quill-Weave to earn the skill level
Return to the guild hall and speak to Azzan about your advancement to be promoted to the Apprentice rank.