How to add newlines into variables in bash script

You can put literal newlines within single quotes (in any Bourne/POSIX-style shell).

str='Hello World
===========
'

For a multiline string, here documents are often convenient. The string is fed as input to a command.

mycommand <<'EOF'
Hello World
===========
EOF

If you want to store the string in a variable, use the cat command in a command substitution. The newline character(s) at the end of the string will be stripped by the command substitution. If you want to retain the final newlines, put a stopper at the end and strip it away afterward. In POSIX-compliant shells, you can write str=$(cat <<'EOF'); str=${str%a} followed by the heredoc proper, but bash requires the heredoc to appear before the closing parenthesis.

str=$(cat <<'EOF'
Hello World
===========
a
EOF
); str=${str%a}

In ksh, bash and zsh, you can use the $'…' quoted form to expand backslash escapes inside the quotes.

str=$'Hello World\n===========\n'

Are you using "echo"? Try "echo -e".

echo -e "Hello World\n===========\n"

you need to do it this way:

STR=$(echo -ne "Hello World\n===========\n")

Update:

As Fred pointed it out, this way you will loose trailing "\n". To assign variable with backslash sequences expanded, do:

STR=$'Hello World\n===========\n\n'

let's test it:

echo "[[$STR]]"

gives us now:

[[Hello World
===========

]]

Note, that $'' is different than $"". The second does translation according to current locale. For deital see QUOTING section in man bash.