This introductory talk will cover several basic elements of convex analysis, with particular attention paid to Fenchel conjugation and infimal convolution. The coverage will begin with an introduction to Fenchel conjugation and a consideration of its basic properties. Examples of convex conjugate function pairs will be followed by the introduction of infimal convolution. General properties of infimal convolution will be considered, along with some particular properties of the Moreau envelope case of infimal convolution.