For the second year of my government and politics A-level we used Political Ideologies: an Introduction by Andrew Heywood. It gives quite a comprehensive explanation of the main political ideologies as well as a number of other political thoughts. Its primary use is as a a-level textbook aimed at those aged 16-18 but as i said it is surprisingly comprehensive. The book explores the origins, key individuals and theorists, history, modern uses, key ideas and tenets, and branches of each ideology.

The ideologies it covers (in the 4th edition) are liberalism, conservatism, socialism, anarchism, fascism, nationalism, feminism, ecologism, religious fundamentalism, and multiculturalism (I checked the newer 6th edition online and it seems to have slightly different ones such as 'green ideology' as opposed to 'ecologism' and 'Islamism' rather than fundamentalism). As you can see, some of these may not strike you immediately as a "political ideology" in its own right but it still gives a relatively detailed explanation of the development and uses of each nonetheless and also gives a 'further reading' list at the end of each ideology.

Capitalism is explored in liberalism, and communism (and it's various forms) in socialism. As a textbook widely used in schools it would be expected to be almost entirely impartial and unbiased.

It should also be noted that there would be alternatives to this book given that it is a school textbook however, it is the most widely used text book on ideologies used in British schools. But even though it is a textbook, it will certainly serve your purpose and the introduction gives an explanation of 'right' and 'left'.

Also, if possible a book (if its not explained in the same book) that explains what actually is (or the different views and arguments for and against) about left/right. Since some people will define a particular ideology (lets say, communism) as "left" and others as "right" and same goes for other ideologies.