The first part of this short course is a general introduction to image compression. We describe the basic structure of an image encoder and discuss its desirable properties. We describe various transforms that have led to various image compression algorithms such as JPEG, JPEG2000 and HD Photo/JPEG XR---specifically, block DCT, wavelets, and lapped transforms. The second part of the tutorial is a more in-depth look at the HD Photo compression algorithm (recently standardized as JPEG XR) developed by Microsoft Corporation. We describe various aspects of the algorithm and, whenever possible, discuss its modules in the context of the corresponding modules of the JPEG compression standard. We conclude by presenting a comparative performance analysis of HD Photo, JPEG2000, SPIHT and JPEG, using both PSNR and the perceptual SSIM index as distortion metrics. (Please define the acronyms SPIHT, PSNR, SSIM, and any other acronyms you may use in the Learning Outcomes or other areas of the description.)