Q:

I often see tutorials online that connect various commands with different symbols. For example:

command1 |  command2
command1 &  command2
command1 || command2    
command1 && command2

Others seem to be connecting commands to files:

command1  > file1
command1  >> file1

What are these things? What are they called? What do they do? Are there more of them?

A:

These are called shell operators and yes, there are more of them. I will give a brief overview of the most common among the two major classes, control operators and redirection operators, and how they work with respect to the bash shell.