The idea of “self” in Buddhism How does Buddhism define “self?” I read in some book that Buddha would avoid such questions, but I wonder why.
The Buddha never avoided it. All that occurred here is there was a teaching (SN 44.10) where the Buddha refused to answer certain wrongly put questions by a confused individual. 

The Buddha taught: 


The underlying tendency to form "self-views" lies within every new born baby (MN 64)
"Self" is an ignorant assumption that is a mental fabrication or deluded thought (SN 22.81) 
The arising of this "self" thought or view is the arising of suffering (SN 12.15; SN 5.10)
This "self" idea is a "disease" - Ud 3.10 
This "self" idea is a cancer, dart &amp; affliction - MN 140



  This world is burning. Afflicted by contact, it calls disease a 'self.'
  
  Ud 3.10
  
  
  
  Bhikkhu, ‘I am’ is a conceiving; ‘I am this’ is a conceiving; ‘I shall be’ is a conceiving; ‘I shall not be’ is a conceiving; ‘I shall
  be possessed of form’ is a conceiving; ‘I shall be formless’ is a
  conceiving; ‘I shall be percipient’ is a conceiving; ‘I shall be
  non-percipient’ is a conceiving; ‘I shall be
  neither-percipient-nor-non-percipient’ is a conceiving. Conceiving is
  a disease, conceiving is a tumour, conceiving is a dart. By overcoming
  all conceivings, bhikkhu, one is called a sage at peace.
  
  MN 140