Despite being an international alphabet, the IPA is based on the Latin alphabet with a few Greek letters thrown in, and the majority of the Latin alphabet is pronounced in the same way it is in Romance languages. Many of its other letters are rotated versions of other Latin letters, which was a choice made to minimize the amount of additional type that would need to be made for printing presses, as you can print a ɯ by turning an m upside-down, for instance.

There's a certain logic to the choice of symbols; the aforementioned sound /ɯ/ for example (IPA transcriptions--that is, written things meant to represent sound as opposed to writing, a distinction important to linguists) is similar to /u/, and as such the symbol ⟨ɯ⟩ (angle brackets, properly ⟨⟩ but commonly <>, are used to refer to the symbol itself, as opposed to the sound it represents) is similar to ⟨u⟩.

Newly invented letters are rare, and usually represent sounds that are utterly unfamiliar to European languages, like /!/ and /ʘ/, which are almost exclusively found in the Khoisan and Bantu language families of sub-Saharan Africa.

The IPA has no uppercase letters. A few sounds, such as /ʙ/, are represented with small capitals, but ordinary capital letters are reserved for other uses; for instance, C is commonly used to mean "any consonant", V for "any vowel", N for "any nasal consonant", and so on.