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The most established method of reconstructing neural circuits from animals involves slicing tissue very thin, then taking mosaics of electron microscope (EM) images. To trace neurons across different images and through different sections, these images must be accurately aligned, both with the others in the same section and to the sections above and below. Unfortunately, sectioning and imaging are not ideal processes - some of the problems that make alignment difficult include lens distortion, tissue shrinkage during imaging, tears and folds in the sectioned tissue, and dust and other artifacts. In addition the data sets are large (hundreds of thousands of images) and each image must be aligned with many neighbors, so the process must be automated and reliable. This paper discusses methods of dealing with these problems, with numeric results describing the accuracy of the resulting alignments.