See man test.
[ "$A" = "Mr Flibble" ] # is the same as
test "$A" = "Mr Flibble"( EXPRESSION ) # EXPRESSION is true
! EXPRESSION # EXPRESSION is false
EXPRESSION1 -a EXPRESSION2 # both EXPRESSION1 and EXPRESSION2 are true
EXPRESSION1 -o EXPRESSION2 # either EXPRESSION1 or EXPRESSION2 is true
-n STRING # the length of STRING is nonzero
STRING # equivalent to -n STRING
-z STRING # the length of STRING is zero
STRING1 = STRING2 # the strings are equal
STRING1 != STRING2 # the strings are not equal
INTEGER1 -eq INTEGER2 # INTEGER1 is equal to INTEGER2
INTEGER1 -ge INTEGER2 # INTEGER1 is greater than or equal to INTEGER2
INTEGER1 -gt INTEGER2 # INTEGER1 is greater than INTEGER2
INTEGER1 -le INTEGER2 # INTEGER1 is less than or equal to INTEGER2
INTEGER1 -lt INTEGER2 # INTEGER1 is less than INTEGER2
INTEGER1 -ne INTEGER2 # INTEGER1 is not equal to INTEGER2
FILE1 -ef FILE2 # FILE1 and FILE2 have the same device and inode numbers
FILE1 -nt FILE2 # FILE1 is newer (modification date) than FILE2
FILE1 -ot FILE2 # FILE1 is older than FILE2
-b FILE # FILE exists and is block special
-c FILE # FILE exists and is character special
-d FILE # FILE exists and is a directory
-e FILE # FILE exists
-f FILE # FILE exists and is a regular file
-g FILE # FILE exists and is set-group-ID
-G FILE # FILE exists and is owned by the effective group ID
-h FILE # FILE exists and is a symbolic link (same as -L)
-k FILE # FILE exists and has its sticky bit set
-L FILE # FILE exists and is a symbolic link (same as -h)
-O FILE # FILE exists and is owned by the effective user ID
-p FILE # FILE exists and is a named pipe
-r FILE # FILE exists and read permission is granted
-s FILE # FILE exists and has a size greater than zero
-S FILE # FILE exists and is a socket
-t FD # file descriptor FD is opened on a terminal
-u FILE # FILE exists and its set-user-ID bit is set
-w FILE # FILE exists and write permission is granted
-x FILE # FILE exists and execute (or search) permission is granted