This book and its sequel （Theories of Matter， Space and Time： Quantum Theories） grew out of courses that we have both taught as part of the third and fourth year of the undergraduate degree programme in Physics at Southampton University， UK. Our goal was to guide the full MPhys undergraduate cohort through some of the trickier areas of theoretical physics that we expect our undergraduates to master. In particular the aim is to move beyond the initial courses in classical mechanics， special relativity， electromagnetism and quantum theory to more sophisticated views of these subjects and their interdependence. Our approach is to keep the analysis as concise and physical as possible whilst revealing the key elegance in each subject we discuss.
　　In this book we first introduce the key areas of the principle of least action， an alternative treatment of Newtonian dynamics， that provides new understanding of conservation laws. In particular here we show how the formalism evolved from Fermat's principle of least time in optics. In the second chapter we introduce special relativity leading quickly to the need and form of four-vectors. We develop four-vectors for all kinematic variables and generalize Newton's second law to the relativistic environment. We return to the principle of least action for a free relativistic particle. The third chapter presents a review of the integral and differential forms of Maxwell's equations before massaging them to four-vector form so that the Lorentz boost properties of electric and magnetic fields are transparent. Again we return to the action principle to formulate minimal substitution for an electrically charged particle.