A markup language is a system for annotating a document in a way that is syntactically distinguishable from the text, allowing for the structured presentation and formatting of information. Markup languages use tags or symbols to define elements within the text, such as headings, paragraphs, links, images, and other components. The most widely known markup language is HTML (HyperText Markup Language), which is used to create and structure content on the web. Other examples include XML (eXtensible Markup Language), which is used for data representation and storage, and Markdown, a lightweight markup language that allows for easy formatting of plain text. Markup languages are essential for enabling browsers and other software to interpret and display content appropriately, facilitating both human-readable and machine-readable formats.

Don't forget TeX and LaTeX. These typesetting markup languages have unparalleled orthogonality and extensibility, and are the only tool for serious mathematical display. They also feature a rich macro-creation environment for creating new user-defined markup, and the TeX typesetting program is considered by many to the most elegant piece of code, anywhere, ever.

No surprise: it was created by Donald Knuth

Markup Languages are a means of embedding additional information within a document, beyond that contained in the "pure" document content.

The term originates from the days when computer documents were prepared from existing paper documents. The first part of the process was to take a hand- or type-written page and manually write on it (i.e. mark it up with) the appropriate formatting commands. These, along with the document content, would then be entered onto the computer.

IBM is responsible for some early work on generalised markup languages (GMLs), including its mainframe product SCRIPT. SGML - standard generalised markup language - is derived from this early work.

SGML derivatives (and, indeed, GML and other IBM markups) depend on a DTD, or Document Type Definition. This defines the markup "tags" and how they can be used. In most cases, the presentation of the information is also specified in the DTD definitions of the tags. However, XML relies on a separate means of supplying layout information - style sheets.

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