This paper gives a notion of harmonic nodal maps from the stratified Riemann surfaces into compact Riemannian manifold, and shows that the space of energy minimizing nodal maps is sequentially compact. It is often difficult to keep track of how topology changes when a sequence of harmonic maps contains a subsequence which converges to a limit map. By making some new and very useful observations on the compactness for 2-dimensional harmonic maps, the authors give a new result, providing a complete understanding of the behavior of the minimizing sequence along the “necks” which connect those harmonic components. Moreover, they give an existence result for energy minimizing nodal maps. In particular, they provide a detailed analysis on the convergence of critical points of the Sacks-Uhlenbeck functional. A general existence theorem for minimal surfaces with arbitrary genus in any compact Riemannian manifold is also provided. For related results see [J. Sacks and K. Uhlenbeck, Ann. Math., II. Ser. 113, 1-24 (1981; Zbl 0462.58014) and Trans. Am. Math. Soc. 271, 639-652 (1982; Zbl 0527.58008)], [R. Schoen and S.-T. Yan, Ann. Math., II. Ser. 110, 127-142 (1979; Zbl 0431.53051)], [M. Gromov, Invent. Math. 82, 307-347 (1985; Zbl 0592.53025)], and [J. Eells and J. C. Wood, Adv. Math. 49, 217-263 (1983; Zbl 0528.58007)].