There are two approaches to category theory, most books, such as those under 'expert' below assume quite a wide knowledge of mathematics. They give lots of examples from different structures to help the reader to 'abstract out' the categorical concepts.
The following two books, both co-authored by F. William Lawvere, are aimed at relative newcomers to mathematics. Although they are not trivial and I think they are useful for a wide range of readers.
|Conceptual Mathematics - This is a book about category theory that does not assume an extensive knowledge over a wide area of mathematics. The style of the book is a bit quirky though.|
|Sets for Mathematics - This is a book about sets from category theory point of view.|
|Categorical Theory - This book is a general introduction to the subject, a bit easier than the Saunders Mac Lane book but still very theoretical.|
Category Theory and Logic
|J. Lambek, P. J. Scott - 1988 - Introduction to Higher-Order Categorical Logic - show that typed lambda-calculi and cartesian closed categories are essentially the same and intuitionistic logic is closely related to topos theory.|
Category Theory and Type Theory
|Categorical Logic and Type Theory - This book is about logic, type theory and category theory. It assumes the reader is familiar with category theory concepts such as adjunctions, limits and CCCs.|
|Categories for Types - This book takes a category theory approach to types and a bit easier pace than the B.Jacobs book.|