what are the differences between a automatic and a manual transmission??

1) A lot fewer components to go bad

2) Usually, depending on how you drive, manual transmissions over you better fuel economy.

3) A manual transmission can be used to slow you car down on downhill slopes (downshifting) which will minimize the need to use your brakes.

4) You can pretend like your Mario Andretti quick shifting like a race car driver. (ha-ha)

Actually manual is better in my opinion. They usually get better gas mileage and have lower maintenance. Also with a manual a dead battery doesn't mean you are stuck. The only benefit of having a automatic is not changing the gears yourself, but they use way more oil (transmission fluid), have more internal parts to break and require a cooler which sits near the radiator (the piping can leak leaving you stranded).

in the automatic mode the car itself shifts the gear whereas in manual mode u have to change the gear.

You might better off asking what common between them.

Other that its application (both are used to take the power and speed from the engine to the wheels, at the best combination possible) they are completely different in design, components size, weight, etc.

Manual are slightly better on gas and are less expensive then automatics.

I'm not an expert but you'll have more control of the car and it's speed with manual. Plus you'll look cooler doing manual, if a girl sees you driving automatic she'll be like WTF.