Font formats were a constant source of technical problems, ever since digital fonts came into use. Luckily, the situation has gotten much better over the last years. Discussing all the existing font formats would take a full course of its own, so we keep it as short as possible for the purpose of this course.
For desktop use, i.e. fonts you install on your local device, avoid using outdated font formats like PostScript Type 1 and other formats which need versions specifically made for certain operating system.
You can recognize fonts that work across operating systems bei their file suffix TTF or OTF.
Font users often have misconceptions about what the suffixes TTF and OTF mean, but the important thing to remember is that both suffixes mean that the font files are usually safe to use with any modern operating system and most apps on that system.
For webfonts, the format of choice today is the Web Open Font Format (WOFF). When you buy a webfont license for commercial fonts, you will usually get an optimized package with WOFF files from the type foundry or the reseller webshop. Webfont services like Google Fonts or Adobe Fonts will automatically deliver these formats to the browsers of your website visitors. It is also possible to convert desktop font formats to WOFF, but make sure the license agreement allows this before making such a conversion.