Do all HTML tags require both a begin and end tag?

No, some tags do not come in pair.

For an example: <img> tag and <br> tag do not require end tags.

Learn more about the similar topics:

Tutorials
HTML Elements and Tags

Exercises & Assignments
Write a program to create a webpage to print values 1 to 5
Write a program to create a webpage to print your city name in red color.
Write a program to print a paragraph with different font and color.