The maximum size is 1500 Bytes. Is there a lower limit? 1? 64? Must it be a multiple of two? Is there somewhere I can look to learn more?
Yes, IPv4 implementations require a minimum MTU of 68 bytes per RFC 791.
See Peter's answer for more detail.
The minimum MTU for IPv4 is 68 bytes. Specifically from https://tools.ietf.org/html/rfc791
Every internet module must be able to forward a datagram of 68 octets without further fragmentation. This is because an internet header may be up to 60 octets, and the minimum fragment is 8 octets.
However such a low MTU would be extremely inefficient.
IPv6 sets a much higher minimum of 1280 bytes and requires links that can't support that MTU to provide a link-specific fragmentation and reassembly layer. From https://tools.ietf.org/html/rfc2460
IPv6 requires that every link in the internet have an MTU of 1280 octets or greater. On any link that cannot convey a 1280-octet packet in one piece, link-specific fragmentation and reassembly must be provided at a layer below IPv6.
Presumablly the motivation is to stop low MTU links from driving inefficiency across the network. I assume 1280 bytes was chosen to allow for a packet to be wrapped in some encapsulation/tunneling crap and still fit in a standard ethernet frame.