This book focuses on important mathematical considerations in describing the synthesis of original mechanisms for generating curves. The synthesis is manual and not based on the use of computer tools. Kinematics is applied to confirm the drawing of the curves, and the closed loop method, and in some cases the distances method, is applied in this phase. The book provides all the notions of structure and kinematics that are necessary to calculate the mechanisms and also analyzes other kinematic possibilities of the created mechanisms. Offering a concise, yet self-contained guide to the mathematical fundamentals for mechanisms of curve generation, together with a useful collection of mechanisms exercises, the book is intended for students learning about mechanism kinematics, as well as engineers dealing with mechanism design and analysis. It is based on the authors' many years of research, which has been published in different books and journals, mainly, but not exclusively, in Romanian.