Following are a few types of puzzle we are often see:

Cryptic
These are very common puzzles and the ones we can see in an escape room. The goal is to find a phrase or a solution to a problem using clever and logical techniques. They are designed to be solved by a single person (some of them), and they can be very simple or complex.
Mechanical
The best example of this puzzle is Rubik’s’ Cube. It is an extremely common type you can see today. They come in various options but all of them require trial and error to solve it. You will need to push move and connect pieces in order to solve it.
Logic
Logic puzzles have a grid of some kind that must be filled properly. There are rules and the solution is usually completely unique. These puzzles may come with a partially filled grid, which makes the solution easier to find.
Trivia
As you may know already, trivia puzzles are based on trivia on any topic and area in the world. They can be found as a part of escape room puzzles, and they may be extremely difficult unless you are familiar with the niche.
Math
Math puzzles are based on math, obviously. They use algorithms (not simple ones), and the main purpose is to test the math skills of a student. There are many tricks and tips you can use but in general, you need to be proficient with math to solve one.
Riddles
Riddles are based on a piece of text containing the question. You need the answer, which is hard and can come in multiple options. There is some logic involved in all of this, but not necessarily. Some riddles are extremely complicated to solve, and there is no common logic present. Being proficient with a particular niche may help you sometimes.
Pattern Guessing
An example of this puzzle is ‘’Find the next number in line 1, 2, 8, 9…’’. They are very old puzzles, and they are very common. The goal is to deduce the outcome from the provided numbers or letters and to use logic or math to find it without an error.
Word puzzles
Word puzzles are common, and you have been playing with them the entire life. The best example is a crossword. Keep in mind that some of these puzzles may have a mathematical nature and foundation.