The use of diffractive and gradient-index (GRIN) lenses as components of imaging optical systems has been investigated for several decades. The elements have proved competitive in their unique focusing and aberration properties and in terms of their additional degrees of freedom for optical design. This book systematically examines the physical principles of diffractive and GRIN elements. Contents: - Introduction to Theory of Diffractive Elements - Introduction to Theory of Gradient-Index Elements - Ray Tracing and Estimation of Image Quality - Aberration Calculations of Homogeneous Optical Systems - Aberration Calculations of Inhomogeneous Optical Systems - Correction Capabilities of Optical Elements of Different Types - High-Resolution Objectives Using Diffractive Lenses - Homogeneous Hybrid Optical Systems - Hybrid Objectives Using Gradient-Index Lenses - Design of Diffractive Lenses from the Point of View of Their Fabrication