This book fills a gap in the literature. So far there has been no book which deals with inertia and gravitation by explicitly addressing open questions and issues which have been hampering the proper understanding of these phenomena. The book places a strong emphasis on the physical understanding of the main aspects and features of inertia and gravitation. It discusses questions such as: (i) Are inertial forces fictitious or real? (ii) Does special relativity provide an insight into the origin of inertia? (iii) Does mass increase relativistically? (iv) Why is the inertial mass equivalent to the gravitational mass? (v) Are gravitational phenomena caused by gravitational interaction according to general relativity? (vi) Is there gravitational energy? (vii) Do gravitational waves carry gravitational energy? (viii) Can gravity be quantized? October 19, 2019: new printing -- an Appendix ``On Relativistic Mass'' is included, some notes and references are added and noticed typos are corrected.