计算满足各种条件的代数曲线和簇的数量是计数代数几何中的一个基本问题，而Schubert演算法是解决此类问题的系统和有效的理论。这个理论是由Schubert发展起来的，本书给出了他对这一理论最全面和最通俗易懂的阐述。从一开始，Schubert演算法理论就吸引了许多伟大的数学家的注意。例如，Hilbert提出了关于Schubert演算法的严格论证，作为他著名的23个问题列表中的第15问题。弦理论的最新发展有助于解决计数几何学中一些悬而未决的问题，因此重新燃起了学者们对这一主题的兴趣。Schubert的这部经典著作的英译本对于初学者和计数几何学专家来说都是最有价值和最有趣的，读者可以通过阅读本书了解Schubert如何思考这些问题以及他如何提出解决这些问题的方法。正如Schubert所说，这本书“应该让读者熟悉一个新的几何领域的思想、问题和成果”，并且“应该教授如何处理一种奇特的演算方法，使人们能够以简单自然的方式确定大量的几何数以及奇点数之间的关系”。

前辅文
Part I The symbolism of conditions
  S1 The number of constants of a structure
  S2 The description of the conditions
  S3 The dimension of a condition and the level of a system
  S4 The principle of conservation of numbers
  S5 The representation of the numbers of condiscretionary- ditions by the symbols of conditions, and computations with these symbols
  S6 The equations between the elementary conditions of each of the three principal elements
Part II The incidence formulae
  S7 The incidence formulae for points and lines
  S8 Applications of incidence formulae (I), (II) and (III) to the incidence of a tangent with its point of contact
  S9 Further examples for the incidence formulae (I), (II), (III)
  S10 The remaining incidence formulae
  S11 Examples for the incidence formulae (IV) to (XIV)
  S12 Application of the incidence formulae to systems of principal elements incident with principal elements
Part III The coincidence formulae
  S13 The coincidence formulae of a pair of points and Bezout's theorems
  S14 Application of the coincidence formulae of S13 to determine the numbers concerning contacts of planar curves and surfaces
  S15 The pair of lines and its coincidence conditions
  S16 Application of the coincidence formulae for pairs of lines to the two ruled families lying on a surface of degree two [23]
  S17 The pairs of distinct principal elements and the coincidence conditions
  S18 Derivation of the Cayley-Brill correspondence formula from the general coincidence formulae for pairs of points
Part IV The computations of numbers via degeneracies
  S19 Numbers for structures consisting of finitely many principal elements
  S20 Numbers for conic sections [30]
  S21 The reduction of Chasles and Zeuthen [32]
  S22 Numbers for surfaces of degree two [33]
  S23 Numbers for cubic planar curves with cusp [34]
  S24 Numbers for cubic planar curves with double point [34]
  S25 Numbers for cubic space curves [35]
  S26 Numbers for planar curves of order four in a fixed plane
  S27 Numbers for the linear congruence [40]
  S28 Numbers for structures consisting of two lines whose points and planes are projective [41]
  S29 Numbers for structures consisting of a pencil of planes and a pencil of lines projective to it [41]
  S30 Numbers for the structure consisting of two projective pencils of lines [41]
  S31 Numbers for structure consisting of two collinear bundles [42]
  S32 Numbers for structures consisting of two correlative bundles [42]
Part V The multiple coincidences
  S33 Coincidence of intersection points of a line and a surface [43]
  S34 The coincidence of multiple points on a line [48]
  S35 The coincidence of multiple lines of a pencil of lines [48]
  S36 Singularities of the generic line complex [49]
Part VI The theory of characteristics
  S37 The problem of characteristics for an arbitrary structure Gamma
  S38 The problem of characteristics for the conic section [51]
  S39 Derivation and application of the characteristic formulae for the structure consisting of a line and a point on it [52]
  S40 Derivation and application of the characteristic formula for the pencil of lines [52]
  S41 Derivation and application of the characteristic formula for the structure consisting of a line, a point on that line, and a plane through that line [52]
  S42 The theory of characteristics of the structure consisting of a line and n points on it [53]
  S43 Computation of the numbers for multiple secants of the intersection curve of two surfaces
  S44 Theory of characteristics of the structure consisting of a pencil of lines and n lines in it. Application to congruences common to two complexes
Remarks on the literature
Index
Author index