explain Oscillator, Phase shift oscillator, How phase shift oscillator work

In order for a circuit to function as an oscillator, it must satisfy the Barkhausen Criteria:
1. The loop gain must be 1
2. The loop phase must be a multiple of 360 degrees.
The second condition is obvious - the output must be fed back into the input in phase with the input signal so that the amplitude of the input is increased.

The diagram below shows a block diagram of a simple oscillator. It consists of an amplifier whose output is fed back to its input through a resonator that provides the appropriate phase shift. The diagram shows the output waveforms for three different values of loop gain.
 

"Phase shift oscillator" is the term given to a particular oscillator circuit topology that uses an RC network in the feedback loop of a tube, transistor, or opamp to generate the required phase shift at a particular frequency to sustain oscillations.  They are moderately stable in frequency and amplitude, and very easy to design and construct.

Phase shift oscillators are most commonly used in tremolo circuits in guitar amplifiers. They are used as the low-frequency oscillator (LFO) that generates the sinusoidal waveform which amplitude modulates the guitar signal to produce the characteristic tremolo amplitude variations.

In order to create and sustain an oscillation at a particular frequency, a circuit must have a gain higher than unity, and a total phase shift around the loop of 360 degrees (which is equivalent to 0 degrees, or positive feedback).  When used with a single-stage inverting amplification element, such as a tube, transistor, or inverting op amp configuration, the amplifier itself provides 180 degrees of phase shift (a gain of -A, where A is the gain of the amplification stage). The remaining 180 degrees of phase shift necessary to provide a total of 360 degrees is provided by an external network of resistors and capacitors.