Numismatics

Numismatics is the study and collecting of coins and the history behind the coins. A Numismatist is either a collector of coins or a scholar who studies the history of coins.
Origin of Word.
The term comes from a word meaning "of coins." The original word is French (numismatique), which itself is from a Latin origin (numismatis).
History of Numismatics.
Coin collectors may have existed in ancient times. Caesar Augustus may have been an example. The first known book about coin collecting was in 1514, "De Asse et Partibus", by Guillaume Budé. However, only royalty really enjoyed coin collecting until the 19th century. That's when professional organizations started to sprout, like the American Numismatic Society in 1858.
Modern Numismatics.
Modern numismatics is a sub-field that focuses on when coins started being stamped by machines (around 17th century on). Because of its focus, modern numismatics is more popular with collectors than with historians. Other subfields/variants include exonumia (focus on coin-like objects), notaphily (focus on paper money instead of coins), and scripophily (focus on stocks and bonds instead of coins).