Chapter headings and selected parts: Preface. Complex Ecological Data Sets. Numerical analysis of ecological data. Statistical testing by permutation. Ecological descriptors. Matrix Algebra: A Summary. The ecological data matrix. Vectors and scaling. Eigenvalues and eigenvectors. Dimensional Analysis in Ecology. Fundamental principles and the Pi theorem. Scale factors and models. Multidimensional Quantitative Data. Multidimensional variables and dispersion matrix. Multinormal distribution. Tests of normality and multinormality. Multidimensional Semiquantitative data. Nonparametric statistics. Quantitative, semiquantitative, and qualitative multivariates. Multidimensional Qualitative Data. Multiway contingency tables. Species diversity. Ecological Resemblance. The basis for clustering and ordination. Association coefficients. R mode: coefficients of dependence. Cluster Analysis. The basic model: single linkage clustering. Cophenetic matrix and ultrametric property. Hierarchical divisive clustering. Ordination in Reduced Space. Projecting data sets in a few dimensions. Principal component analysis (PCA). Nonmetric multidimensional scaling (MDS). Interpretation of Ecological Structures. Ecological structures. The mathematics of ecological interpretation. The 4th-corner problem. Canonical Analysis. Redundancy analysis (RDA). Canonical correspondence analysis (CCA). Canonical analysis of species data. Ecological Data Series. Characteristics of data series and research objectives. Trend extraction and numerical filters. Periodic variabilty: spectral analysis. Detection of discontinuities on multivariate series. Box-Jenkins models. Spatial Analysis. Unconstrained and constrained ordination maps. Causal modelling: partial canonical analysis. Causal modelling: partial Mantel analysis. Bibliography. Tables. Subject index.