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An excellent set of resourecs on geophysics and inversion - University of British Columbia Geophysical Inversion Facility
Alex Kaminsky's ZOND geophysical inversion software. Includes 1D, 2D and 3D resistivity and IP codes. Zond Geophysical Software
Thomas Lecoq's geophysics web and blog python scripts and more
Moscow State University - software for DC resistivity and IP. Contains freeware for VES.

Albert Tarantola's well established text - Inverse Problem Theory

Some useful software and publications on biomedical imaging from the Scientific and Imaging Institute at the University of Utah - SCI
ParaView - open source data visualisation software - ParaView
Mayavi - powerful visualisation software - Mayavi2
Finite element mesh generator - Tetgen
Mesh generator with graphical interface - Gmsh
Fast 2D triangular mesh generator - Triangulator
EIDORS: Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software - EIDORS

UK Groundwater Forum - UKGF
USGS Groundwater Software - USGS
HOBE - Center for Hydrology, Hydrological Observatory, University of Copenhagen HOBE
Hytool: Philippe Renard's open source matlab toolbox for well test interpretation Hytool
FEFLOW modelling software FEFLOW

Archived presentations from workshops and short courses
Hydrogeophysics over multiple scales: talk given by Andrew Binley at the 4th Cargèse Summer School: Flow and Transport in Porous and Fractured Media, 25 June - 7 July 2018, Cargèse, Corsica.
Integrated Hydrogeophysical Inversion workshop, Banff, Canada, 2008 - Workshop report
Presentations at the EAGE Near Surface 2005 workshop on Hydrogeophysics - Palermo2005
Andrew Binley's lectures at the FIVA PhD course on Hydrogeophysics at the University of Copenhagen 2006 - FIVA Hydrogeophysics 2006