Aiming to provide an understanding of fundamental science concepts, and to give a basic mechanical, thermal and electrical engineering systems background for student engineers, this text covers the GNVQ Engineering mandatory units "Science and Mathematics for Engineering" (intermediate) and "Science for Engineering" (advanced). However, it can be regarded as a basic textbook in engineering science for a much wider range of courses. The aims are to describe engineering systems in terms of basic scientific laws and principles, to investigate the behaviour of simple linear systems in engineering, to calculate the response of engineering systems to changes in variables, and to determine the response of engineering systems to changes in parameters. It is assumed that the reader has little previous knowledge of each topic that is considered and the emphasis is on "practicality and learning by example". Theory is introduced in each chapter by a reasonably brief outline of essential definitions, formulae, laws, and procedures. 500 worked problems, 325 multiple-choice questions (this being the form expected of students for National testing of their "Science for Engineering" units), and 400 short answer questions and 700 further questions with answers are included. The problems mirror practical situations found in science and engineering.