We introduce som e resultson Cayley graphs obtained by a group ofresearchers atXinjiang University or finished in coorperation w ith others since 1995.The results are m ainly aboutthe isom orphism s and autom or- phism s
the connectivity and ham iltonicity ofCayley graphs as w ellas the fundam entalproperties ofrandom Cayley graphs.Atthe end ofthis paper