This is the sequel to Problems in Mathematical Analysis I: Real Numbers, Sequences and Series (volume 4 in the AMS series, the Student Mathematical Library). As in the first volume, this book is divided into two parts. The first is a collection of exercises and problems, and the second contains their solutions. The book mainly deals with real functions of one real variable. Topics include: properties of continuous functions, intermediate value property, uniform continuity, mean value theorems, Taylor's formula, convex functions, sequences and series of functions.