This text covers four major topics of integrated photonics: fundamental principles of electromagnetic theory; waveguides; simulation of waveguide modes; and photonic structures. The first part of the text explores the basis for optical propagation and establishes the use of the MKS system, discussing the wave equation and the properties of materials such as attenuation and dispersion. The next section explores the operation of optical waveguides. It starts with planar slab waveguides, then systematically advances to more complicated structures, such as graded index waveguides, circular waveguides, and rectangular waveguides. The details of coupling light between and within waveguide modes is clearly described, and applied to the examination of photonic bandgap crystals and optical devices such as arrayed waveguides. The final section of the text discusses optoelectronic devices such as modulators and switches. These topics are very active areas of research and are likely to increase in significance as they mature. From the beginning, the book introduces numerical techniques for studying non-analytic structures. Most chapters have numerical problems designed for solution using a computational program such as Matlab or Mathematica. An entire chapter is devoted to one of the numeric simulation techniques being used in optoelectronic design (the Beam Propagation Method), and provides opportunity for students to explore some novel optical structures without too much effort. Small pieces of code are supplied where appropriate to get the reader started on the numeric work. This text is designed for the senior/first year graduate student, and requires a basic familiarity with electromagnetic waves, and the ability to solve differential equations with boundary conditions.