Expressions (Linux in a Nutshell, 4th Edition)

Operator	Description
=	Assign value.
+= -=	Reassign after addition/subtraction.
*= /= %=	Reassign after multiplication/division/remainder.
&= ^= \|=	Reassign after bitwise AND/XOR/OR.
++	Increment.
--	Decrement.

Operator	Description
* / %	Multiplication; integer division; modulus (remainder).
+ -	Addition; subtraction.

Operator	Description
~	Binary inversion (one's complement).
!	Logical negation.
<< >>	Bitwise left shift; bitwise right shift.
&	Bitwise AND.
^	Bitwise exclusive OR.
\|	Bitwise OR.
&&	Logical AND.
\|\|	Logical OR.
{ command }	Return 1 if command is successful, 0 otherwise. Note that this is the opposite of command's normal return code. The $status variable may be more practical.

Operator	Description
= = !=	Equality; inequality.
<= >=	Less than or equal to; greater than or equal to.
< >	Less than; greater than.

Operator	Description
-b file	The file is a block special file.
-c file	The file is a character special file.
-d file	The file is a directory.
-e file	The file exists.
-f file	The file is a plain file.
-g file	The file's set-group-ID bit is set.
-k file	The file's sticky bit is set.
-l file	The file is a symbolic link.
-L file	Apply any remaining operators to symbolic link, not the file it points to.
-o file	The user owns the file.
-p file	The file is a named pipe (FIFO).
-r file	The user has read permission.
-s file	The file has nonzero size.
-S file	The file is a socket special file.
-t file	file is a digit and is an open file descriptor for a terminal device.
-u file	The file's set-user-ID bit is set.
-w file	The user has write permission.
-x file	The user has execute permission.
-X file	The file is executable and is in the path, or is a shell built-in.
-z file	The file has 0 size.
!	Reverse the sense of any preceding inquiry.

Finally, tcsh provides the following operators, which return other kinds of information:

Operator	Description
-A[:] file	Last time file was accessed, as the number of seconds since the epoch. With a colon (:), the result is in timestamp format.
-C[:] file	Last time inode was modified. With a colon (:), the result is in timestamp format.
-D file	Device number.
-F file	Composite file identifier, in the form device:inode.
-G[:] file	Numeric group ID for the file. With a colon (:), the result is the group name if known, otherwise the numeric group ID.
-I file	Inode number.
-L file	The name of the file pointed to by symbolic link file.
-M[:] file	Last time file was modified. With a colon (:), the result is in timestamp format.
-N file	Number of hard links.
-P[:] file	Permissions in octal, without leading 0. With a colon (:), the result includes a leading 0.
-Pmode[:] file	Equivalent to -P file ANDed to mode. With a colon (:), the result includes a leading 0.
-U[:] file	Numeric user ID of the file's owner. With a colon (:), the result is the username if known, otherwise the numeric user ID.
-Z file	The file's size, in bytes.

8.5. Expressions