The valuative tree This&nbsp;volume is devoted to a beautiful object called the valuative tree and designed as a powerful tool for the study of singularities in two complex dimensions. Its intricate yet manageable structure can be analyzed by both algebraic and geometric means. Many types of singularities including those of curves ideals and plurisubharmonic functions can be encoded in terms of positive measures on the valuative tree. The construction of these measures uses a natural tree Laplace operator of independent interest. TOC:Introduction. 1. Generalities. 2. MacLanes Method. 3. Tree Structures. 4. Valuations Through Puiseux&nbsp;Series. 5. Topologies. 6. The Universal Dual Graph. 7. Tree Measures. 8. Applications of the Tree Analysis. Appendix. References. Index.&nbsp;&nbsp