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These notes are an outgrowth of an advanced undergraduate course taught at the University of Maryland, College Park. They are intended as an introduction to various aspects of particle and nuclear physics with an emphasis on the role of symmetry. The basic philosophy is to introduce many of the fundamental ideas in nuclear and particle physics using relatively sophisticated mathematical tools -- but to do so in as a simplified a context to explain the underlying ideas. Thus, for example, the Higgs mechanism is discussed in terms of an Abelian Higgs model. The emphasis is largely, but not entirely theoretical in orientation. The goal is for readers to develop an understanding of many of the underlying issues in a relatively sophisticated way.