Separation of the elements of classical mechanics into kinematics and dynamics is an uncommon tutorial approach‎,‎ but the author uses it to advantage in this two‎-volume set‎.‎ Students gain a mastery of kinematics first a solid foundation for the later study of the free‎-body formulation of the dynamics problem‎.‎ A key objective of these volumes‎,‎ which present a vector treatment of the principles of mechanics‎,‎ is to help the student gain confidence in transforming problems into appropriate mathematical language that may be manipulated to give useful physical conclusions or specific numerical results‎.‎ In the first volume‎,‎ the elements of vector calculus and the matrix algebra are reviewed in appendices‎.‎ Unusual mathematical topics‎,‎ such as singularity functions and some elements of tensor analysis‎,‎ are introduced within the text‎.‎ A logical and systematic building of well‎-known kinematic concepts‎,‎ theorems‎,‎ and formulas‎,‎ illustrated by examples and problems‎,‎ is presented offering insights into both fundamentals and applications‎.‎ Problems amplify the material and pave the way for advanced study of topics in mechanical design analysis‎,‎ advanced kinematics of mechanisms and analytical dynamics‎,‎ mechanical vibrations and controls‎,‎ and continuum mechanics of solids and fluids‎.‎ Volume I of Principles of Engineering Mechanics provides the basis for a stimulating and rewarding one‎-term course for advanced undergraduate and first‎-year graduate students specializing in mechanics‎,‎ engineering science‎,‎ engineering physics‎,‎ applied mathematics‎,‎ materials science‎,‎ and mechanical‎,‎ aerospace‎,‎ and civil engineering‎.‎ Professionals working in related fields of applied mathematics will find it a practical review and a quick reference for questions involving basic kinematics‎.‎ ‎"‎