What Are The Three Main Types Of Authority In An Organisation?

Your question is a little confusing, since you have mentioned types of authority and types of organization as well. The types of authority are different from types of organization. However here is a brief overview:  Types of Authority depends on level of management and is divided in three layers i.e  Top level  Middle Level  Functional Level  Whereas types of organization depend on their organizational structure and are as follows:  -Functional organization  - Matrix organization  - Divisional organization  For details see the link below  Organization

I believe you are concerned about the three types of authority as described by the Max Weber. The three main types of authority, as discussed by him are as follows:
1: Traditional Authority: It is derived from customers, rituals and habits. It is passed from one generation to the next.
2. Rational-Legal authority: It is established by formal rules and laws of state. They are very complex and are in documented form.
3: Charismatic Authority: It is based on the charisma of the leader or an individual. It depends on the grace of a person and the way he carries himself.

Traditional authority n its based on the customers rituals n habits.its passed to one generation to another generation.
Rational legal its established by formal  rules and laws of taste.
Charismatic .its based on the charisma of the leader an individual.it depends on the grace of a person n the way he carries himself.

Types of authority

1. Business Development: This authority is the backbone of the company.

2. Technical Staff:

3. Management: Last but not the least, a good management can make a average team work better

Line Authority - represented by the chain of command
Staff Authority - Advisory authority
Functional Authority - allows managers to direct specific processes or policies affecting in other departments

Traditional, behaviorist, functional

Traditional; charismatic; rational-legal

This is the right issue valid instructions which other must follow.