International Trade and Investment Theories are critical for understanding the patterns and dynamics of global economic interactions. Over the years, various ideas have been created to explain the motivations and benefits of international trade and investment. Here are several significant hypotheses:

Mercantilism: One of the earliest philosophies of international trade, it was developed between the 16th and 18th century. It implies that a country should endeavor to accumulate wealth by increasing exports while decreasing imports. The emphasis is on maintaining a favorable trade balance in order to grow the country's gold reserves and increase its power and influence.

Absolute Advantage : Absolute advantage is a theory proposed by Adam Smith in his seminal work "The Wealth of Nations" (1776) that states that countries should concentrate in providing commodities and services in which they have an absolute productivity advantage over other countries. By exchanging these goods, both countries can gain better efficiency and a wider range of products.

Comparative Advantage : Comparative advantage is a theory introduced by David Ricardo in the early nineteenth century that builds on absolute advantage. It contends that even if one country is more efficient in producing all products than another, both can benefit from trade if one specializes in producing goods with lower opportunity costs (foregone production of other goods). 

Heckscher-Ohlin Theory: Developed in the early twentieth century by Eli Heckscher and Bertil Ohlin, this theory emphasizes that a country's factor endowments, such as labor, capital, and land, shape the pattern of international trade. Countries will export items that make extensive use of abundant factors and buy goods that make extensive use of scarce factors.

New Trade Theory: Proposed in the 1970s and 1980s by Paul Krugman and others, the New Trade Theory emphasizes on economies of scale and product differentiation. It implies that, due to economies of scale, certain industries may concentrate in a few countries, even if other countries could produce the same commodities with comparable efficiency.

Porter's Diamond Model : Michael Porter developed the Porter's Diamond Model, which examines a country's competitiveness in specific industries. Factor conditions (e.g., skilled labor, infrastructure), demand conditions, linked and supporting sectors, and firm strategy, structure, and rivalry are all included in the diamond model. It aims to explain why various industries flourish in specific countries.

There are various ideas that explain the flow of capital across borders in terms of investment:

Internalization Theory: This theory, also known as the Market Imperfections Theory, contends that firms choose to internalize overseas operations when the costs of accessing the market (such as licensing or franchising) are greater than the costs of managing foreign operations directly.

 International Product Life Cycle Theory : Raymond Vernon developed the International Product Life Cycle Theory, which describes how products progress through several stages of production and marketing. As a product grows, production may transfer from its native country to another, resulting in international investment patterns.

Eclectic Paradigm (OLI Model): Developed by John Dunning, this model combines three criteria to explain why corporations choose to invest abroad: ownership, location, and internalization. It implies that enterprises must have special advantages, that the location in which they invest must have specific advantages, and that internalization should be more advantageous than other kinds of market entry.

These theories have influenced how economists and policymakers think about international trade and investment. They provide vital insights into the reasons for global economic relationships, resource distribution, and so on.