1) To make yourself familiar with
2) Achieve success in
3) To conclude things with great success, or with great fanfare
4) To look at something with great admiration or desire
5) A rut is something that has become tediously repetitive, the same thing day after day. To life oneself out of the rut is to make a conscious effort to do something different, or at least approach your daily tasks with a different attitude so that you're not so bored.