The Modbus protocol was invented by Modicon (now a division of Schneider Electric), and is now administered by modbus.org. Modicon/Schneider/modbus.org have published five documents describing the Modbus protocol:

Modbus Protocol Reference Guide. PI-MBUS-300. Rev J. June 1996. This is the original Modbus specification, which has been superceded by the current Modbus specification and the serial specification listed below. This document is referred to as the original Modbus specification.

Open Modbus/TCP Specification. Andy Swales. Release 1.0. March 1999. This document specifies how Modbus messages are sent over a network using the TCP/IP protocols. It also contains some intelligent commentary on the Modbus protocol, and an appendix on client and server implementation, which may be useful if this area is new to you. Surprisingly, this document does not appear to be available from the official Modbus web-site. This document is referred to as the Modbus/TCP specification.

Modbus Application Protocol. V1.1b3. April 2012. This is the current definition of Modbus function codes and the format of the corresponding request and response messages. It does not cover how these messages are packaged in the RTU, ASCII or TCP variants of the protocol. This document is referred to as the current Modbus specification.

Modbus Messaging on TCP/IP Implementation Guide. Rev 1.0b. December 2006. This consists mainly of what appear to be design notes for Modicon's (?) implementation of Modbus/TCP. You will probably find it hard to read if you don't already have a good understanding of the area, and not very useful if you do. It is, however, the only document on the official Modbus web-site that contains (in section 3.1) a description of the Modbus/TCP protocol. This document is referred to as the Modbus/TCP implementation guide.

Modbus over Serial Line - Specification & Implementation Guide. V1.02. December 2006. This is the current definition of the RTU and ASCII variants of the Modbus protocol. It also contains physical layer (electrical) specifications. This document is referred to as the serial specification.