Introduction:
Under the Indian Income Tax Act, there are various categories of persons who are chargeable to tax. These categories define the legal entities or groups that are subject to taxation in India. However, one of the given options, 'Foreign Corporation', is not a category of person chargeable to tax under the Indian Income Tax Act.

Explanation:
Here is an explanation of each category of person chargeable to tax under the Indian Income Tax Act:

1. Association of Persons (AOP):
An Association of Persons (AOP) refers to a group of individuals or entities who join together for a common purpose with the intention of earning income. This category includes partnerships, joint ventures, and other associations. AOPs are taxable entities under the Income Tax Act and are required to file their income tax returns.

2. Artificial Judicial Person:
Artificial Judicial Person refers to entities such as local authorities, statutory corporations, and government bodies. These entities are created by law and have a separate legal existence. They are treated as separate entities for tax purposes and are subject to taxation under the Income Tax Act.

3. Foreign Corporation:
Foreign corporations are companies or legal entities that are incorporated outside of India. They are not considered as a category of person chargeable to tax under the Indian Income Tax Act. However, their income earned in India may be subject to taxation under the provisions of the Act, depending on the nature of the income and the applicability of tax treaties.

4. Hindu Undivided Family (HUF):
A Hindu Undivided Family (HUF) is a separate tax entity that consists of a family governed by Hindu law and having joint family property. HUFs are treated as separate entities for tax purposes, and their income is taxed separately from the income of individual members of the family.

Conclusion:
In conclusion, the category of person chargeable to tax under the Indian Income Tax Act that is not included in the given options is 'Foreign Corporation'. While foreign corporations may be subject to taxation on their income earned in India, they are not specifically categorized as chargeable to tax under the Act.