Introduction: Linking Earth Sciences and Mathematics -- A Review of Earthquake Statistics: Fault and Seismicity-Based Models, ETAS and BASS -- A Finite Element Algorithm of a Nonlinear Diffusive Climate Energy Balance Model -- An Upper Limit to Ground Deformation in the Island of Tenerife, Canary Islands, for the Period 1997-2006 -- Multi-Channel Satellite Image Analysis Using a Variational Approach -- 3D Gravity Inversion by Growing Bodies and Shaping Layers at Mt. Vesuvius (Southern Italy) -- Testing Logselfsimilarity of Soil Particle Size Distribution: Simulation with Minimum Inputs -- Steric Sea-Level Change and its Impact on the Gravity Field caused by Global Climate Change -- A Fractal Interaction Model for Winding Paths through Complex Distributions: Application to Soil Drainage Networks -- The Coherent Pixels Technique (CPT): An Advanced DInSAR Technique for Nonlinear Deformation Monitoring -- On the Occurence of Extreme Events in Long-term Correlated and Multifractal Data Sets -- A Regional Archaeomagnetic Model for the Palaeointensity in Europe for the last 2000 Years and its Implications for Climatic Change. A Complutense International Seminar on "Earth Sciences and Mathematics" was organised and held in Madrid at the Facultad de Ciencias Matemáticas of the Universidad Complutense de Madrid September, 13th-15th, 2006. Scientists from both fields, Mathematics and Earth Sciences, took part in this International Seminar, addressing scientific problems related with our planet from clearly complementary approaches, seeking to gain and learn from this dual approach and proposing a closer collaboration in the near future. This volume is the first one of a Topical Issue on "Earth Sciences and Mathematics" and contains papers addressing different topics as deformation modelling applied to natural hazards, inverse gravimetric problem to determine 3D density structure, advanced differential SAR interferometry, climate change, geomagnetic field, Earthquake statistics, meteorological studies using satellite images, climate energy balance models, study of soils properties, and multifractal data sets.