Vojtěch Janoušek (*1968) is associate professor at the Charles University in Prague, employed in the radiogenic isotopes laboratory of the Czech Geological Survey. He received a MSci from the Charles University and a PhD in geochemistry from the University of Glasgow. His research focusses on igneous geochemistry, geochronology and numerical modelling as well as computing in geosciences. He is editor-in-chief of open-access Journal of Geosciences.Jean-François Moyen is professor at the University of Saint-Etienne, France. He obtained a PhD in petrology and geochemistry at the University of Clermont-Ferrand (France), and was a post-doc and then lecturer in Stellenbosch, South Africa (2003–2009). His research interests include geochemical modelling, igneous petrology and geochemistry.Hervé Martin is Professor at the University Blaise Pascal in Clermont-Ferrand, France, where he works in the “Laboratoire Magmas et Volcans”. The research that he develops consists inmodeling the geochemical behaviour of major and trace elements in order to constrain the petrogenesis of the Earth’s primitive continental crust, as well as magma genesis in modern subduction zones.Vojtěch Erban is working at the Radiogenic Isotopes Laboratory of the Czech Geological Survey in Prague. His professional interests comprise geochemistry, isotope analytics and geochemical modelling.Colin Farrow is an IT specialist and former member of the Department of Geology & Applied Geology, University of Glasgow with an interest in developing software for geological data analysis.

• 1 Introduction.- Part I R/GCDkit at work.- 2 Data manipulation and simple calculations.- 3 Classical plots.- 4 Specialized plots.- 5 Radiogenic isotopes.- Part II Modelling major elements.- 6 Direct models.- 7 Reverse models.- 8 Forward modelling in R.- 9 Reverse modelling in R.- Part III Modelling trace elements.- 10 Dilute trace elements: partition coefficients.- 11 Direct (dilute) trace-element models.- 12 Reverse (dilute) trace-element models.- 13 Trace elements as essential structural constituents of accessory minerals: the solubility concept.- 14 Forward modelling in R.- 15 Reverse modelling in R.- Part IV Radiogenic isotopes.- 16 Direct models.- 17 Reverse models.- 18 Forward modelling in R.- 19 Reverse modelling in R.- Part V Practical modelling.- 20 Choosing an appropriate model.- 21 Semi-quantitative geochemical approach.- 22 Constraining a model.- 23 Numerical tips and tricks.- 24 Common sense in action.- Part VI Worked examples.- 25 Differentiation of a calc-alkaline volcanic series: example of the Atacazo-Ninahuilca volcanoes, Ecuador.- 26 Progressive melting of a metasedimentary sequence: the Saint-Malo migmatitic complex, France.- Appendix I R syntax in a nutshell.- Appendix II Introduction to GCDkit.- Appendix III Solving systems of linear algebraic equations in R.

“It is a textbook which discusses the theory of geochemical modelling as applied to whole-rock major and trace element data and to radiogenic isotopes … . A starting graduate student in geochemistry would benefit from spending time with this book. It is well produced, the text is clear and the coding sections are printed in a different font for clarity, it is well illustrated with excellent diagrams, some of which are in colour, and each chapter is thoroughly referenced.” (Hugh Rollinson, Elements, elementsmagazine.org, June, 2016)

Vojtěch Janoušek (*1968) is associate professor at the Charles University in Prague, employed in the radiogenic isotopes laboratory of the Czech Geological Survey. He received a MSci from the Charles University and a PhD in geochemistry from the University of Glasgow. His research focusses on igneous geochemistry, geochronology and numerical modelling as well as computing in geosciences. He is editor-in-chief of open-access Journal of Geosciences.Jean-François Moyen is professor at the University of Saint-Etienne, France. He obtained a PhD in petrology and geochemistry at the University of Clermont-Ferrand (France), and was a post-doc and then lecturer in Stellenbosch, South Africa (2003–2009). His research interests include geochemical modelling, igneous petrology and geochemistry.Hervé Martin is Professor at the University Blaise Pascal in Clermont-Ferrand, France, where he works in the “Laboratoire Magmas et Volcans”. The research that he develops consists inmodeling the geochemical behaviour of major and trace elements in order to constrain the petrogenesis of the Earth’s primitive continental crust, as well as magma genesis in modern subduction zones.Vojtěch Erban is working at the Radiogenic Isotopes Laboratory of the Czech Geological Survey in Prague. His professional interests comprise geochemistry, isotope analytics and geochemical modelling.Colin Farrow is an IT specialist and former member of the Department of Geology & Applied Geology, University of Glasgow with an interest in developing software for geological data analysis.

• 1 Introduction.- Part I R/GCDkit at work.- 2 Data manipulation and simple calculations.- 3 Classical plots.- 4 Specialized plots.- 5 Radiogenic isotopes.- Part II Modelling major elements.- 6 Direct models.- 7 Reverse models.- 8 Forward modelling in R.- 9 Reverse modelling in R.- Part III Modelling trace elements.- 10 Dilute trace elements: partition coefficients.- 11 Direct (dilute) trace-element models.- 12 Reverse (dilute) trace-element models.- 13 Trace elements as essential structural constituents of accessory minerals: the solubility concept.- 14 Forward modelling in R.- 15 Reverse modelling in R.- Part IV Radiogenic isotopes.- 16 Direct models.- 17 Reverse models.- 18 Forward modelling in R.- 19 Reverse modelling in R.- Part V Practical modelling.- 20 Choosing an appropriate model.- 21 Semi-quantitative geochemical approach.- 22 Constraining a model.- 23 Numerical tips and tricks.- 24 Common sense in action.- Part VI Worked examples.- 25 Differentiation of a calc-alkaline volcanic series: example of the Atacazo-Ninahuilca volcanoes, Ecuador.- 26 Progressive melting of a metasedimentary sequence: the Saint-Malo migmatitic complex, France.- Appendix I R syntax in a nutshell.- Appendix II Introduction to GCDkit.- Appendix III Solving systems of linear algebraic equations in R.

“It is a textbook which discusses the theory of geochemical modelling as applied to whole-rock major and trace element data and to radiogenic isotopes … . A starting graduate student in geochemistry would benefit from spending time with this book. It is well produced, the text is clear and the coding sections are printed in a different font for clarity, it is well illustrated with excellent diagrams, some of which are in colour, and each chapter is thoroughly referenced.” (Hugh Rollinson, Elements, elementsmagazine.org, June, 2016)

Vojtěch Janoušek (*1968) is associate professor at the Charles University in Prague, employed in the radiogenic isotopes laboratory of the Czech Geological Survey. He received a MSci from the Charles University and a PhD in geochemistry from the University of Glasgow. His research focusses on igneous geochemistry, geochronology and numerical modelling as well as computing in geosciences. He is editor-in-chief of open-access Journal of Geosciences.Jean-François Moyen is professor at the University of Saint-Etienne, France. He obtained a PhD in petrology and geochemistry at the University of Clermont-Ferrand (France), and was a post-doc and then lecturer in Stellenbosch, South Africa (2003–2009). His research interests include geochemical modelling, igneous petrology and geochemistry.Hervé Martin is Professor at the University Blaise Pascal in Clermont-Ferrand, France, where he works in the “Laboratoire Magmas et Volcans”. The research that he develops consists inmodeling the geochemical behaviour of major and trace elements in order to constrain the petrogenesis of the Earth’s primitive continental crust, as well as magma genesis in modern subduction zones.Vojtěch Erban is working at the Radiogenic Isotopes Laboratory of the Czech Geological Survey in Prague. His professional interests comprise geochemistry, isotope analytics and geochemical modelling.Colin Farrow is an IT specialist and former member of the Department of Geology & Applied Geology, University of Glasgow with an interest in developing software for geological data analysis.

• 1 Introduction.- Part I R/GCDkit at work.- 2 Data manipulation and simple calculations.- 3 Classical plots.- 4 Specialized plots.- 5 Radiogenic isotopes.- Part II Modelling major elements.- 6 Direct models.- 7 Reverse models.- 8 Forward modelling in R.- 9 Reverse modelling in R.- Part III Modelling trace elements.- 10 Dilute trace elements: partition coefficients.- 11 Direct (dilute) trace-element models.- 12 Reverse (dilute) trace-element models.- 13 Trace elements as essential structural constituents of accessory minerals: the solubility concept.- 14 Forward modelling in R.- 15 Reverse modelling in R.- Part IV Radiogenic isotopes.- 16 Direct models.- 17 Reverse models.- 18 Forward modelling in R.- 19 Reverse modelling in R.- Part V Practical modelling.- 20 Choosing an appropriate model.- 21 Semi-quantitative geochemical approach.- 22 Constraining a model.- 23 Numerical tips and tricks.- 24 Common sense in action.- Part VI Worked examples.- 25 Differentiation of a calc-alkaline volcanic series: example of the Atacazo-Ninahuilca volcanoes, Ecuador.- 26 Progressive melting of a metasedimentary sequence: the Saint-Malo migmatitic complex, France.- Appendix I R syntax in a nutshell.- Appendix II Introduction to GCDkit.- Appendix III Solving systems of linear algebraic equations in R.

“It is a textbook which discusses the theory of geochemical modelling as applied to whole-rock major and trace element data and to radiogenic isotopes … . A starting graduate student in geochemistry would benefit from spending time with this book. It is well produced, the text is clear and the coding sections are printed in a different font for clarity, it is well illustrated with excellent diagrams, some of which are in colour, and each chapter is thoroughly referenced.” (Hugh Rollinson, Elements, elementsmagazine.org, June, 2016)