AXIS
It is a linear element that helps to organizing the spaces in a symmetry and create balance. Visual focus and structure are determined with it.
Diagrammatic example:
http://www.whapin.com/wp-content/uploads/2014/04/modern-chandelier-lighting-dining-room-sets-table-wood-luxury-furniture-tableware-decor-chairs-ideas-pendant-light-fixtures-design.jpg
SYMMETRY
It depends on an axis, without it symmetry cant exist. It occurs when the pattern of spaces or objects repeat itself keeping the axis in center, basically cutting them half. There are two types of symmetry; bilateral and radial.
Diagrammatic example:
HIERARCHY
It can be created by having a visual emphasis in the space. There can be three types of hierarchy; by size, by shape and by placement. We see this principle being applied in pretty much most architecture. It helps to identify the importance of the spaces and the roles the spaces play for the users.
Diagrammatic example:
DATUM
It could be a line, plane and volume that deals with grouping elements which may not be related and may be placed in a random pattern. It acts like an axis to organize the elements.
Diagrammatic example:
http://www.design4interior.com/interior-design/doehler-loft-renovation-by-sabo-project.html
RHYTHM
The consistent or varied arrangement of elements or spaces that create a movement as the sequence of spaces and elements.
Diagrammatic example:
https://www.pinterest.com/pin/477522366712296473/
REPETITION
When a pattern continued with a common element,this repetition aids to create a rhythm with the elements or spaces. It can occur by size, shape or detailed characteristics.
Diagrammatic example:
http://minimalist-home-designs.blogspot.com/2010_08_01_archive.html
TRANSFORMATION
It is basically the change in movement or notion of an element or spaces. This transformation can be structural as well.
Diagrammatic example:
www.pintrest.com