The schemaic you provided shows a Pierce Oscillator in the parallel resonance mode - a common IC oscillator configuration.
You have to understand the individual parts of the circuit to understand the whole.
R1 is a negative feedback resistor for the inverting amplifier. Its value is selected to pull the operating point of the amplifier down such that the amplifier stays in the linear portion of its operting range. Without this resistor, the amplifier could either cutoff or saturate when the positive feedback from the crystal circuit is applied to the input.
Y1, and its associated capacitors, form an active resonant circuit. R2 is selected such that, at resonance, the phase shift of the resonant circuit is as close to 180 degrees as possible. R2 and the resonant circuit form a positive feedback path for the inverting amplifier.
Y1 is mechanically piezoelectric, but it has inductive, capacitive, and resistive characteristics. It is those charactersistics that are adjusted/biased by R2 to "tune" the phase shift for optimum (180deg) for positive feedback. R1 keeps the amplifier centered in its operating range by applying negative feedback.