The Dipole
The Dipole was invented by Heinrich Rudolph Hertz it is a relatively simple antenna using wire. The feeder is connected to a Balun which in turn is connected to the two antenna "legs" one being the ground the other the live leg. Usually dipoles are either 1/2 or 1/4 wave. Dipoles can be mounted horizontally or vertically.
Here is a Javascript Dipole Calculator
The Longwire or Random Wire Antenna
As you'd guess this antenna is not measured it is as it says on the can, oft called the Zigzag antenna, due to the fact that it can be zigzagged across the garden. Most longwires are made of 12 or 14 AWG wire. All longwires require a Antenna Tuning Unit (ATU)
The Yagi
Invented by Yagi-Uda in Japan the Yagi is a Directional antenna, the Yagi exhibits more gain than any other antenna, and some amateur Yagis have many directors.
And here is a Javascript Beam/Yagi
calculator