Authority of an agent can arise in a number of ways

Authority of an agent can arise in a number of ways: expressed, impressed and apparent. Express authority is where the principle expressly authorises the agent in relation to a specific contract, which may be written of orally expressed. Implied authority can be demonstrated when an agent has implied authority to do things which are reasonably incidental to the performance of an expressly authorised act. Apparent authority arises where an agent is held out buy the principle as having authority.
When an agent acts beyond the limits of the express authority, the agent will be liable for breach of warranty not only to the principle but they may also be liable to the third party.
So long as an agent acts within the limits of their authority, the agent incurs no liability under the contract. However, an agent may be held personally liable when the agent enters into a contract without discussing the existence of a principle.