Alphabet in kurrent script from about 1865. The next-to-last line shows the umlauts ä, ö, ü, and the corresponding capital letters Ae, Oe, and Ue; and the last line shows the ligatures ch, ck, th, sch, sz, and st.
Danish Kurrent script (»gotisk skrift«) from about 1800 with Æ and Ø at the end of the alphabet
Kurrent is an old form of German language handwriting based on late medieval cursive writing, also known as Kurrentschrift or Alte Deutsche Schrift ("old German script"). Over the history of its use into the first part of the 20th century, many individual letters acquired variant forms.
Sütterlin is a modern script based on Kurrentschrift that is characterized by simplified letters and vertical strokes. It was developed in 1911 and taught in German schools as primary script from 1935 until 1941. Then it was replaced with "normal German font", which is sometimes referred to (correctly but confusingly) as "Latin font". See Ausgangsschrift for examples of post-1941 school handwriting samples.