The Croats have used the Glagolitic alphabet ("glagoljica") in the middle ages. Probably the oldest existing document in Croatian, the Baška tablet carved in stone in the 11th century, was written in Glagolitic script. The first Croatian printed book, the Missal from 1483, was also written in Glagolitic script.
Some believe that this script was created by St. Cyrill in the second half of the 9th century. Also, some of the letters are supposedly similar to the corresponding ones in very old oriental scripts such as South-Semitic, Samaritan (an old Hebrew script), the Cretan linear A and B, Armenian and others.
There seems to have existed a third variant of Glagolitic, the triangular Glagolitic, from which the other two developed. The number of letters in the alphabet doesn't seem to be certain, either: there were 32 to 34 letters. Also, there are about 250 known Croatian Glagolitic ligatures.
For more information about the Croatian Glagolitic script, see