preface 1 hardy-littlewood maximal operator 1.1 hardy-littlewood maximal operator 1.2 calderdn-zygmund decomposition 1.3 marcinkiewicz interpolation theorem 1.4 weighted norm inequalities 1.5 notes and references 2 singular integral operators 2.1 calderon-zygmund singular integral operators 2.2 singular integral operators with homogeneous kernels 2.3 singular integral operators with rough kernels 2.4 commutators of singular integral operators 2.5 notes and references 3 fractional integral operators 3.1 riesz potential 3.2 weighted boundedness of riesz potential 3.3 fractional integral operator with homogeneous kernels 3.4 weighted boundedness of t��,a 3.5 commutators of riesz potential 3.6 commutators of fractional integrals with rough kernels 3.7 notes and references 4 oscillatory singular integrals 4.1 oscillatory singular integrals with homogeneous smooth kernels 4.2 oscillatory singular integrals with rough kernels 4.3 oscillatory singular integrals with standard kernels 4.4 multilinear oscillatory singular integrals with rough kernels 4.5 multilinear oscillatory singular integrals with standard kernels 4.6 notes and references 5 littlewood-paley operator 5.1 littlewood-paley g function 5.2 weighted littlewood-paley theory 5.3 littlewood-paley g function with rough kernel 5.4 notes and references bibliography index