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The Lieb-Liniger model is a prototypical integrable model and has been turnedinto the benchmark physics in theoretical and numerical investigations of lowdimensional quantum systems.  In this note, we present various methods for calculating local and nonlocal$M$-particle correlation functions, momentum distribution and static structurefactor. In particular, using the Bethe ansatz wave function of the strongcoupling Lieb-Liniger model, we analytically calculate two-point correlationfunction, the large moment tail of momentum distribution and static structurefactor of the model in terms of the fractional statistical parameter $\alpha=1-2/\gamma$, where $\gamma$ is the dimensionless interaction strength. We alsodiscuss the Tan's adiabatic relation and other universal relations for thestrongly repulsive Lieb-Liniger model in term of the fractional statisticalparameter.

Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas