Radio is the branch of telecommunication that involves the transmission of electromagnetic waves through space.
James C. Maxwell developed the first radio-wave theory in 1864. He proved, mathematically at least, that if an electrical interruption is of short distance from the point at which it occurred, there would be passage of electrical current due to "some sort of waves that move at the speed of light", in which the electromagnetic energy would travel.
Radio signals are made up of two kinds of waves: “audio” (or sound) waves represent the sounds being sent to the audience and radio frequency waves travel with these sound waves to "carry" them to radios in homes and car, for example. All waves have three parts: a wavelength, an amplitude and a frequency. Each of these parts can be changed to carry information.
AM stands for "Amplitude Modulation", which refers to the means of encoding the audio signal on the carrier frequency. In many countries, AM radio stations are known as "medium wave" (MW) stations, since their frequencies are located in that band (531-1602kHz). In Europe, AM stations are also found in the long wave (LW) band of 153-279kHz. AM stations are also sometimes referred to as "standard broadcast stations", since AM was the was the first form used to transmit broadcast radio signals to the public. Stereophonic AM broadcasting in the USA uses the C-Quam system of encoding the stereo signal. This system has been the official standard since 1993. AM radio can develop problems with interference. This makes it hard to hear the radio show. Interference can be caused by many sources. For example, sparks discharge when a car is started, in electric motors in all sorts of electrical appliances, and even lightning and Sun Spots, all of these things can produce interference to AM radio. There is a lot of background noise that changes the amplitude of the radio wave signal. This creates the random crackling noises call static. 
FM stands for “Frequency modulation”- a type of radio transmission, the frequency of the combined waves change to reproduce the audio signal. For example, higher frequency is associated with the peak amplitude in the audio wave. FM waves do not have a problem with interference because the noise background does not modify the radio wave frequency. In addition FM waves give better sound reproduction. FM radio stations all transmit in a band between 88 megahertz (millions of cycles per second) and 108 megahertz, which used to be known as VHF (Very High Frequency)in Britain and Ireland. The band is divided into 100 channels, each 200 kHz (0.2 MHz) wide. The center frequency is located at 1/2 the bandwidth of the FM Channel, or 100 kHz (0.1 MHz) up from the lower end of the channel. For example, the center frequency for Channel 201 (the first FM channel) is 88.0 MHz + 0.1 MHz = 88.1 MHz. So there can be a station at 88.1 megahertz, 88.3 megahertz, 88.5 megahertz, and so on. The 200-kilohertz spacing, and the fact that they center on odd numbers is completely arbitrary and was decided by the FCC. In Europe, the FM stations are spaced 100 kilohertz apart instead of 200 kilohertz apart, and they can end on even or odd numbers. 
From a purely technical point of view, shortwave radio refers to those frequencies between 3 and 30 MHz. Their main characteristic is their ability to "propagate" (travel) for long distances, making possible such worldwide communications as international broadcasting and coordination of long-distance shipping.
From a social point of view, shortwave radio is a way to find out what the rest of the world thinks is important. Many countries broadcast to the world in English, making it easy to find out what a given country's position is on those things it finds important. Shortwave radio can also provide a way to eavesdrop on the everyday workings of international politics and commerce in distant lands.