This page lists characters used in orthographies based on the Mongolian (Hudum) script and provides information about them.
Character notes have companion pages that summarise how a script is used for a specific orthography. For the Mongolian script, see Mongolian (Traditional Mongolian).
Richard Ishida, Mongolian Character Notes, 12-Nov-2023, https://r12a.github.io/scripts/mong/block
Until I can generate graphics for the tables you should view this document in Firefox, and ideally have Mongolian Baiti font on your system. Safari makes a pig's breakfast of vertical Mongolian text. Chrome does a better job, but fails to maintain cursive connections when a span is used to highlight a character in a sequence.
Unfortunately, browser support for Mongolian is still rather fragile. Fonts typically behave differently from each other with regards to implementing the necessary OpenType rules for Mongolian contextual forms, and don't always do what you'd expect. (In particular, not all of the variant forms are produced by a given font.) Since the examples and tables in this page are not graphics, they may not always reflect what is intended, and are perhaps better treated as small tests, rather than canonical representations.
I found that some fonts didn't interact correctly with the zero width joiner on Safari and Chrome, so I had to resort to using nirugu characters instead.
Variant forms. Many of the characters have variant forms. The number and standard character sequences to create these variants have not yet been completely standardised. Work is going on to resolve this. Where a character has variant forms, you will see a link to another document; that document summarises the latest information I have about intended variation sequences and their support in fonts.
Shape tables. Inside the Mongolian letter descriptions there are also syllable tables, showing what the letter looks like when combined with a vowel. Only the red text is an expected combination for Mongolian – the grey examples are there to simply show what your font does when an unexpected combination appears.