Linux Shell Scripting Tutorial (LSST) v1.05r3
Chapter 3: Shells (bash) structured Language Constructs

test command or [ expr ]

test command or [ expr ] is used to see if an expression is true, and if it is true it return zero(0), otherwise returns nonzero for false.
test expression OR [ expression ]

Following script determine whether given argument number is positive.

$ cat > ispostive
# Script to see whether argument is positive
if test $1 -gt 0
echo "$1 number is positive"

Run it as follows
$ chmod 755 ispostive

$ ispostive 5
5 number is positive

$ispostive -45
Nothing is printed

./ispostive: test: -gt: unary operator expected

Detailed explanation
The line, if test $1 -gt 0 , test to see if first command line argument($1) is greater than 0. If it is true(0) then test will return 0 and output will printed as 5 number is positive but for -45 argument there is no output because our condition is not true(0) (no -45 is not greater than 0) hence echo statement is skipped. And for last statement we have not supplied any argument hence error ./ispostive: test: -gt: unary operator expected, is generated by shell , to avoid such error we can test whether command line argument is supplied or not.

test or [ expr ] works with
1.Integer ( Number without decimal point)
2.File types
3.Character strings

For Mathematics, use following operator in Shell Script

Mathematical Operator in  Shell Script MeaningNormal Arithmetical/ Mathematical StatementsBut in Shell
   For test statement with if commandFor [ expr ] statement with if command
-eqis equal to5 == 6if test 5 -eq 6if [ 5 -eq 6 ]
-ne is not equal to5 != 6if test 5 -ne 6if [ 5 -ne 6 ]
-lt is less than5 < 6if test 5 -lt 6if [ 5 -lt 6 ]
-le is less than or equal to5 <= 6if test 5 -le 6if [ 5 -le 6 ]
-gt is greater than5 > 6if test 5 -gt 6if [ 5 -gt 6 ]
-ge is greater than or equal to5 >= 6if test 5 -ge 6if [ 5 -ge 6 ]

NOTE: == is equal, != is not equal.

For string Comparisons use

string1 = string2string1 is equal to string2
string1 != string2 string1 is NOT equal to string2
string1 string1 is NOT NULL or not defined 
-n string1 string1 is NOT NULL and does exist
-z string1 string1 is NULL and does exist

Shell also test for file and directory types

-s file   Non empty file
-f file   Is File exist or normal file and not a directory 
-d dir    Is Directory exist and not a file
-w file   Is writeable file
-r file    Is read-only file
-x file   Is file is executable

Logical Operators

Logical operators are used to combine two or more condition at a time

Operator            Meaning
! expression Logical NOT
expression1  -a  expression2 Logical AND
expression1  -o  expression2 Logical OR

Decision making in shell script ( i.e. if command)