Three different version of SNMP exist: SNMPv1 (RFC's 1155, 1157, and 1212), SNMPv2c (RFC's 1901 through 1908), and SNMPv3 (RFC's 3411 though 3418). The co-existence of all three versions are detailed in RFC 3584.
SNMPv1 is the original standard for community based management. SNMPv2 was derived from the SNMPv1 framework but had no message definition, which was later revamped aa SNMPv2c, a community based version of SNMPv2 with a message format similar to SNMPv1. SNMPv2 added several new datatypes (Counter32, Counter64, Gauge32, UInteger32, NsapAdress, and BIT STRING), as well as enhancements to OID tables and the setting of OID values. SNMPv3 is an extensable SNMPv2 framework with a new message format, ACL and security abilities, and remote configuration of SNMP parameters.
SNMP is based on several other standards including the Abstract Syntax Notation 1 Basic Encoding Rules (ASN.1 BER) which defines the SNMP used Datatypes and the Structure of Management Information (SMI) which details the grammar used by SNMP MIBs. SMI comes in two varieties: SMIv1 (RFC 1155) and SMIv2 (RFC 2578). SMIv1 is now obsolete and should not be used. If you choose to modify MIBs at some point you'll need to learn SMIv2 and ASN.1 syntax, but otherwise they are interesting but unnecessary to learn.
To this day, SNMPv1 and SNMPv2c are the most commonly used, however due to the insecurity inherent to these protocols read-only access is typical. In general, don't bother with SNMPv3 unless you really need the added security features.