Anno Domini (Latin for in the year of the lord), or A.D., is the period beginning with the year 1. Common Era (C.E.) is an alternative, secular term for this period. B.C., which stands for before christ, covers all time before the year 1 (there is no year 0). Before Common Era (B.C.E.) is an alternative term for this era.
Whether to include the periods or to leave them off (e.g., AD, CE, etc.) is a matter of preference. Some publishers use the periods, and some don’t.