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I am looking to hone my skills in the theory and the mathematicas involving the projections systems, projection transformations ( from xy to uv, φλ and vice versa).

Can you share the books/pdfs/online-references that you have read and found them useful?

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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).

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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.

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The following book is pretty good if you work in an ArcGIS environment.

Working with Projections and Datum Transformations in ArcGIS

It´s a good introduction if you are new to the subject but goes into detail where necessary.

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