Concept:
The study of ancient writing systems, scripts, inscriptions, and the development of scripts is known as Paleography.
Paleography helps scholars understand how letters, alphabets, and writing styles changed over time.
Step 1: Understand the meaning of the question.
The question asks about the study of the development of script.
Script means written symbols or letters used in a language.
For example:
\[
\text{Brahmi script, Kharosthi script, Devanagari script}
\]
The scientific study of such scripts is called Paleography.
Step 2: Check the given options.
Paleobotany is the study of ancient plants.
Photogrammetry is related to measurement using photographs.
Paleontology is the study of fossils.
Paleography is the study of ancient scripts and handwriting.
Step 3: Final conclusion.
Therefore, the study of development of script is called:
\[
\boxed{\text{Paleography}}
\]