Multiset table algebra is considered. The notion of a table specified using the notion of a multiset (or bag). A signature of multiset table algebra is filled up with new operations such as inner and outer joins, semi-join and aggregate operations. A formal mathematical semantics of these operations is defined. The special element NULL is inserted in the universal domain for a define of the outer join. Keywords—relation databases; multiset table algebra; inner joins; outer joins; semi-join, aggregate operations