Right now only typekit is the only font provider available in Muse. Please view this article for more details.
Adding more info.
The fonts are available in muse are free font but you can add more fonts to your site from typekit. Please check.
Similarly you can check with other providers but method would be different.
Thank you for your reply Kumar. Unfortunately it was completely unhelpful.
From my original question:
" I'm forced to use a couple of fonts that Typekit does not provide"
"Will Muse be supporting other font providers than Typekit?"
"Will Muse allow us to host our own fonts?"
I understand that Typekit is owned by Adobe and you would prefer to lock out the competition but until Typekit offers every single font available this policy works against the interest of the user.
Also, Muse is marketed as 'Websites without coding". Having to add code manually into my site's HTML is coding.
Please refer to https://typekit.com/foundries for information regarding requesting a typeface or foundry. If you would like your custom corporate typeface to be added to Typekit library, you may contact firstname.lastname@example.org.
The Typekit collection as well as the subset available in Muse will keep growing over time to meet the requirements of its userbase.
At this time, Reklame Script is not available as a web font in Muse.
Please see http://forums.adobe.com/message/4451491#4451491 for more details on our future plans to augment the web font selection inMuse.