This book is about Ritt operators on Banach spaces, with important developments concerning their functional calculus, square functions, and dilation properties. Ritt operators and their functional calculus have natural connections with various topics such as semigroups and sectorial operators. However, in this monograph, Ritt operators are considered on their own right. A special emphasis is given to Ritt operators acting on either Hilbert spaces, Lp-spaces or non-commutative Lp-spaces.Researchers wishing to familiarize themselves with Ritt operators and their properties will find this book a valuable resource. A number of appendices are included, providing necessary background information and making the topic accessible to a wide mathematical audience.