Birds are not mammals. They belong to the "class" called "Birds."
Scientific information is split into a number of levels: Kingdom, Phylum, Class, Order, Family, Genus, Species. (one silly way to remember this is King Phillip, Come Out For Goodness Sake!)
All of the scientific information about a living thing is called it's "Taxonomy"
So, for example, if you're talking about a Trumpeter Swan, it's taxonomy is:
Kingdom: animal (scientific name: Regnum animale)
Phylum: animals with a backbone (scientific name: Chordata)
Class: Bird (scientific name: Aves)
Order: Water fowl (scientific name: Anseriformes)
The five most well known classes of vertebrates (animals with backbones) are mammals, birds, fish, reptiles, amphibians. They are all part of the phylum chordata -- I remember "chordota" by thinking of spinal chord.