The Buddha And His Teachings
By Venerable Narada Maha Thera
A comprehensive book on the story of Buddha and his teachings. The first fourteen chapters are about Buddha’s life. Chapter 15 is, “What is Buddhism.” Chapter 16 is on the Characteristics of Buddhism. In chapters 17 through 44, the Venerable author explains Buddha’s teachings. I learned Buddhism from this book. The book is a great source of information for those who wish to understand the life of the Buddha and the fundamentals of his teachings.
What The Buddha Taught
By Venerable Walpola Rahula Maha Thera
This book delves into the philosophy, essentials, and fundamentals of Buddhism. The first chapter preps the mindset of the reader (especially one who is new to Buddhism) to understand the Dhamma. The second chapter explains the Four Noble Truths, which are the fundamental doctrine of Buddhism. The Buddha stated that the road to enlightenment is through the Four Noble Truths. The book then goes into other subjects, such as Karma, Rebirth, Mindfulness, the doctrine of no soul…I was fascinated by the way the Venerable author is able to deliver a complex subject in a concise, yet understandable, manner.
My recommendation is for you to read The Buddha and His Teachings first. Follow that up with What The Buddha Taught.