We consider the class H0 of sense-preserving harmonic functions f = h + \bar g defined in the unit disk |z| < 1 and normalized so that h(0) = 0 = h′(0) − 1 and g(0) = 0 = g′(0), where h and g are analytic in the unit disk. In the first part of the article we present two classes PH0(α) and GH0(β) of functions from H0 and show that if f \in PH0(α) and F \in GH0(β), then the harmonic convolution is a univalent and close-to-convex harmonic function in the unit disk provided certain conditions for parameters α and β are satisfied. In the second part we study the harmonic sections (partial sums) {s_{n,n}}\left( f \right)\left( z \right) = {s_n}\left( h \right)\left( z \right) + \overline {{s_n}\left( g \right)\left( z \right)} , where f = h + \bar g \in H0, sn(h) and sn(g) denote the n-th partial sums of h and g, respectively. We prove, among others, that if f = h + \bar g \in H0 is a univalent harmonic convex mapping, then sn,n(f) is univalent and close-to-convex in the disk |z| < 1/4 for n ≥ 2, and sn,n(f) is also convex in the disk |z| < 1/4 for n ≥ 2 and n ≠ 3. Moreover, we show that the section s3,3(f) of f \in CH0 is not convex in the disk |z| < 1/4 but it is convex in a smaller disk., Liulan Li, Saminathan Ponnusamy., and Obsahuje seznam literatury