Entomology is the study of insects

An entomologist is someone who studies insects in general.

A lepidopterist studies Lepidoptera (butterflies and moths).

A coleopterist studies coleoptera (beetles).

Here are some more insect orders (groups):

Ephemeroptera – Mayflies
Odonata – Dragonflies
Plecoptera – Stoneflies
Orthoptera – Crickets and grasshoppers
Phasmida – Stick and leaf insects
Dermaptera – Earwigs
Dictyoptera – Cockroaches and mantids
Isoptera – Termites
Psocoptera – Booklice and barklice
Mallophaga – Biting lice
Anoplura – Sucking lice
Hemiptera – True bugs
Thysanoptera – Thrips
Neuroptera – Lacewings, alder flies and snake flies
Mecoptera – Scorpion flies
Trichoptera – Caddis flies
Diptera – True flies
Siphonaptera – Fleas
Hymenoptera – Bees, wasps, ants, sawflies, ichneumons and others

An arachnologist studies arachnids (not insects)