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The reference (in the US, at least) is John Snyder's Map Projections--A Working Manual. The entire monograph is available as a Google book. Introductory sections give the theory. The theory is accessible to someone with a working knowledge of multivariate calculus. Emphasis is on documenting formulas, primarily series expansions needed for subsequent ...

I've always referred to "Map Projections: A Working Manual", 1987, Snyder, John P. USGS Professional Paper: 1395 which is available as a PDF to download.

More detailed and with all the information you need, the Coordinate Conversions and Transformations including Formulas document gives you a detailed explanation of the map projections and the formulas necessary for executing coordinate conversions and transformations (suported by the EPSG dataset).

I liked Datums and Map Projections: For Remote Sensing, GIS and Surveying from Jonathan IIiffe and Roger Lott. Make sure you grab the second edition. However, it still has some errors. Nevertheless you get some examples to practice.