With such a self explanatory name, you can deduce that intergovernmental relations are the relations in an intergovermental level. To further simplify, these are local, provincial, and national institutions creating an interacting network to empower the different parts of government to cling in a way pretty much suitable to respective institutional plans.
The society in which they are apart
The governmental institutions of which they are in part
Only the external conditions which shape the life of the given country at a particular time
The constitutional regime within which they are set
Federal-State Relations
Local-Federal Relations
State-Local Relations
Inter-Local Relations
Legislative
The Executives
National Inclusive Forum
Judiciary
Property, business, and family
Safety, family, and business
Health, property, and business
Property, health, and safety
The provision of undergraduate and postgraduate education
The provision of elementary and secondary education
The recruitment of military personnel
The appointment of the Supreme Court Justice
Horizontal
Sectoral
Transverse
Vertical
Unitary system
Republic
Representative democracy
Constitutional monarchy
Parliamentary system
Dual Federalism
Picket Fence Federalism
Fiscal Federalism
Cooperative Federalism
Harvey C. Mansfield
Helen Margetts
Theda Skocpol
Deil S. Wright
Public Services
Private Services
Political Parties
Interest Groups