Some authors present a table of contents, but if it is a standard paper with the sections that are specified below, this is redundant. Again, the object is still to lead the reader deeper and deeper into the paper. Now it is time to carefully introduce the topic and this is done in a section with a heading such as preliminaries . All of the precise definitions are here along with any previous results that shall be needed later in the paper. All notation should be explained and necessary background information should be presented here.
Simple examples are always welcome.
Lists of extremely terse scientific definitions with very little prose are quite hard on the reader and can be very discouraging. Remember that you're still telling a story and trying to help the reader to easily understand what comes later. Next we encounter what we have been waiting for, the main event. It could be called main results or given a section heading that describes what is contained therein. The reader should be led smoothly through the design of the proof or algorithm that is being shown in public for the first time.