You can execute the scripts in $ROOTSYS/tutorials (or sub-directories)
by setting your current directory in the script directory or from any
user directory with write access.
Several tutorials create new files. If you have write access to
the tutorials directory, the new files will be created in the tutorials
directory, otherwise they will be created in the user directory.

You can start by executing the standard ROOT demos with a session like
  root > .x demos.C
or
  root > .x $ROOTSYS/tutorials/demos.C

You can execute the standard ROOT graphics benchmark with
  root > .x benchmarks.C
or
  root > .x $ROOTSYS/tutorials/benchmarks.C

The $ROOTSYS/tutorials directory include several sub-directories

-fft:      Fast Fourier Transform with the fftw package
-fit:      Several examples illustrating minimization/fitting 
-foam:     Random generator in multi-dimensional space
-geom:     Examples of use of the geometry package (TGeo classes)
-gl:       Visualisation with OpenGL
-graphics: Basic graphics
-graphs:   Use of TGraph, TGraphErrors, etc
-gui:      Scripts to create Graphics User Interface
-hist:     Histograming
-image:    Image Processing
-io:       Input/Output
-math:     Maths and Statistics functions
-matrix:   Matrices (TMatrix) examples
-mlp:      Neural networks with TMultiLayerPerceptron
-net:      Network classes (client/server examples)
-physics:  LorentzVectors, phase space
-pyroot:   python tutorials
-pythia:   Example with pythia6
-quadp:    Quadratic Programming
-ruby:     ruby tutorials
-smatrix:  Matrices with a templated package
-spectrum: Peak finder, background, deconvolutions
-splot:    Example of the TSplot class (signal/background estimator)
-sql:      Interfaces to SQL (mysql, oracle, etc)
-thread:   Using Threads
-tmva:     Examples of the MultiVariate Analysis classes
-tree:     Creating Trees, Playing with Trees
-unuran:   Interface with the unuram random generator library
-xml:      Writing/Reading xml files