Walkman is a Sony brand tradename originally used for portable audio cassette/tape players in the late 1970s.
Discman was the product name given to Sony's first portable CD player, the D-5 (North America and various other countries)/D-50, which was the first on the market in 1984, and adopted for Sony's entire portable CD player line.
In 1992 Sony released the Sony MiniDisc, a system with (recordable) 'mini-discs' that could contain around 80 minutes of audio.
The first MP3 player was developed in the early 1990s by Frauenhofer, but this player was unsuccessful. In 1997 Tomislav Uzelac of Advanced Multimedia Products invented the AMP MP3 Playback Engine, which is recognized as the first successful MP3 Player.
Apple iPod 1G
In 2001 Apple released the first iPod model (the first models were released in collaboration with HP, so there's also a HP iPod).