The Multiplicity of Mutations in Human Cancers -- Monitoring Chromosome Rearrangements -- Nucleotide Excision Repair and its Connection with Cancer and Ageing -- DNA Mismatch Repair and Colon Cancer -- Base Excision Repair -- Genomic Instability in Cancer Development -- Translesion Synthesis And Errorprone Polymerases -- The INK4A/Arf Network - Cell Cycle Checkpoint or Emergency Brake? -- DNA Replication and Genomic Instability -- The Dream of Every Chromosome: Equal Segregation for a Healthy Life of the Host -- Telomere Structural Dynamics in Genome Integrity Control and Carcinogenesis -- Gene Amplification Mechanisms -- DNA Methylation and Cancer-associated Genetic Instability -- Deregulation of the Centrosome Cycle and the Origin of Chromosomal Instability in Cancer -- Mammalian DNA Damage Response Pathway -- ATM and Cellular Response to DNA Damage -- Mitotic Checkpoint, Aneuploidy and Cancer. Research over the past decades has firmly established the genetic basis of cancer. In particular, studies on animal tumour viruses and chromosome rearrangements in human tumours have concurred to identify so-called 'proto-oncogenes' and 'tumour suppressor genes', whose deregulation promotes carcinogenesis. These important findings not only explain the occurrence of certain hereditary tumours, but they also set the stage for the development of anti-cancer drugs that specifically target activated oncogenes. However, in spite of tremendous progress towards the elucidation of key signalling pathways involved in carcinogenesis, most cancers continue to elude currently available therapies. This stands as a reminder that "cancer" is an extraordinarily complex disease: although some cancers of the haematopoietic system show only a limited number of characteristic chromosomal aberrations, most solid tumours display a myriad of genetic changes and considerable genetic heterogeneity. This is thought to reflect a trait commonly referred to as 'genome instability', so that no two cancers are ever likely to display the exact same genetic alterations. Numerical and structural chromosome aberrations were recognised as a hallmark of human tumours for more than a century. Yet, the causes and consequences of these aberrations still remain to be fully understood. In particular, the question of how genome instability impacts on the development of human cancers continues to evoke intense debate.