execises in computational complexity
I had a course held by Jiri Srba a few years ago on basic complexity and computability theory is good, I would say. The second part (Lecture 9 to 15) goes through time and space complexity, shows some important results on the field and has pdf's of both exercises and solutions for each lecture.
It is based on the book "Introduction to the Theory of Computation" by Michael Sipser, which also has a good walkthrough of both topics in general.

Link: https://intranet.cs.aau.dk/education/courses/2010/cc/course-plan/ (owned by Aalborg University)

Good luck!