Inhalt

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   Introduction and motivation
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   The beta-function of QCD
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   Pressure in hot QCD
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   Other applications
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  Reduction to master integrals
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   Notation
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   Momentum shifts
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   Linear relations between integrals
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   Integration by parts
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   Syzygies
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   Mass derivatives and Lorentz invariance
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   Relations between different dimensions
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   Reduction
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   Example: 4-loop sunset
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  Solving master integrals
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   Feynman parameters
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   Sector decomposition
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   Parametric integration and linear reducibility
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   Mellin-Barnes representations
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   Differential equations
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   Dimensional recurrence relations
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   Laporta's method
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   Example: 2-loop sunset
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   Difference equations
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   Laporta's algorithm for difference equations
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   Minimal order reduction algorithm
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   Comparison of reduction algorithms
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   Translation and recurrence relations
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   Translation process
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   Optimising input equations
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   Reducing recurrence relations
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   Evaluation via factorial series
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   Interlude: Fibonacci numbers
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   The general solution
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   Initial conditions
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   Precision and convergence
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   Numerical evaluation in practice
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  Implementation details
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   Reductions
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   Momentum shifts
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   Generation of equations and the r-s-boundaries
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   Rational algebra and parallelisation
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   Numerical runs and delayed subsector execution
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   Choosing a master basis
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   Timings
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   Numerical evaluation
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  The fully massive tadpoles up to 5 loops
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   Classification
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   Results
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   Checks
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   Conclusion and outlook
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   Tadpole classification
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   Reduction statistics
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  Numerical results
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   2-loop
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   3-loop
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   4-loop
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   5-loop
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   References