how to design an AM transmitter and AM receiver?

Are you serious? What is your background and experience in electronics? Why not just purchase an AM transmitter and AM receiver? What frequency range do you want to transmit and receive over? How much power will the transmitter radiate? Licensed or un-licensed operation? Do you want to park a ship a few miles off-shore and start up your own pirate broadcast station? What will you use an AM transmitter and AM receiver for? Do you have a budget with respect to time and cost? And please don't post questions like this on my profile page. I only answer, in the forum, questions like this one posted here for everyone to see.

 

An FM transmitter goes 10 times further with the same output and is much easier to design and has much less background noise.