After applying for a job, if the hiring manager did not contact me after two or three weeks what should i do?

There is no definite answer for this. You can either email them to inquire your status or concentrate on the next available opportunity. Sometimes, employers are busy with other priorities that they may take time to make a decision, so don't be discouraged.

Follow up! Often, hiring managers have many applications and an e-mail or phone call, can get your application to the top of the pile and, at least, get it looked at. You should follow up. They can hear your voice, which connects them to your resume. It's only right to acknowledge someone who has interviewed though I know this is not always done. That's why I would still encourage someone - if they really want the job or think they did a solid interview - to call and ask if a decision has been made. This will allow that person to move on or find out if there is a time frame when they can expect a decision. I tend to be rather assertive in getting information that impacts my life or career.