Bats are mammals.
So, like us and rats, they have hairs, regulate
their body temperature (‘warm blood’), and breastfeed their pups. We, bats and rats belong to the same class of animals, the Mammalia. Birds,
for instance, belong to the class Aves.
Each class is subdivided into orders, and the order that
comprises humans is called Primates, which includes also monkeys, apes, tamarins,
lemurs and marmosets. The order of rats is the Rodentia, and
comprises also capybaras, mice and agoutis.
The bat order is called Chiroptera, which means ‘hands in the shape of wings’
(in Greek: kheir = hand + pteron = wing). Just remember ‘chiropraxis’ and ‘pterosaur’ for
the etymology. This order comprises 18 families and at least
1,116 species (Simmons 2005).
Wings, among vertebrates, are a modification of forelimbs (‘arms’),
thus bats and birds have only two wings (insects may have four). Bat wings are unique, different from bird and pterosaur wings. Bats have five fingers in each hand (like us), birds have three and pterosaurs had
five. The bat body has a large membrane that encompasses four fingers (except for the thumb)
and forms the wing. Bird wings are formed mainly by feathers attached to
forelimbs.
Pterosaur wings were also formed by a membrane, but the size and
shape of their fingers were different from bats. See the figure below.

Further readings:
If you can read Portuguese, there are some excellent articles made
for the general public, which give basic information and destroy
myths. I recommend especially the articles
Cara de Vilão Vida de Mocinho
[Face of a Villain, Life of a Good Guy] (Vieira 2005) Senhores
da Noite [Lords of the Night] (Figueiredo 2007), Desmistificando
Morcegos [Demystifying Bats] (Pinto 2008), and
Anjos Negros [Black Angels] (Bourscheit 2008). There is also
the free book
Morcegos do Brasil [Bats from Brazil] (Reis et al. 2007), with a biological file
for each Brazilian species. For English readers, there is a nice introductory book,
The World of Bats (Richarz & Limbruner 1993), and the
amazing website of
Bat Conservation International.
Visit also the Brazilian Society for the Study of Chiropterans:

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