This book is a logical continuation of our manuscript "Let Us Do Math: Basic Mathematics Level I". It is mainly dedicated to above average students from high-school and first year university, and their mathematics instructors. This book provides first steps for many Mathematics Contests. It can be also considered as a reference book to practice and go deeply in understanding basic mathematics' concepts. Usually instructors do not have the time to cover a large number of situations, this is why our manuscript provides a smooth, easy to read, and self-contained reference that is rich with exercises. It contains about 314 solved problems.