Classical anarchist economics is usually expressed in the economic systems of anarcho-communism, collectivist anarchism and mutualist/individualist anarchism. Economics as a field has been criticized by other fields of academy so anyway lets check all of that.
Anarcho-communism: Mainly the system proposed by people like Kropotkin, Malatesta. A good economist with many writings on that particular subject of this current is the spanish and argentinian anarchist Diego Abad de Santillan who was one of the most important economists during the Spanish revolution of 1936. A good economics work from this tendency is "Fields, factories and workshops" by Kropotkin himslef. Even though Kropotkin was clear in stating a difference between marxism and anarchocomunnism one can any way also check the recent work by "anarcho-marxist" plataformist author Wayne Price "Marx’s Economics for Anarchists"
Collectivist anarchism: Mainly the economic proposal by Mikhail Bakunin and others like the spanish anarchist Ricardo Mella. The proposal of Bakunin was mainly to base distribution of wealth on the labour theory of value instead of what the anarcho-communists proposed which was distribution based on need. Bakunin also advocated workers cooperatives while Anarcho-communism tends towards communal ownership of enterprises. Clearly the most extensive recent exponent of this position as far as economics is Michael Albert and his PARECON system or Participatory Economics.
Individualist anarchism/Mutualism: One should not equate individualist anarchism with a mutualist position since many "egoist" anarchists of the insurrectionist tendency tend towards anarcho-communism just like someone like Luigi Galleani. Nevertheless mutualism should be dealt together with individualist anarchism due to the fact that what the main mutualist economist, Pierre Joseph Proudhon, proposed was something very similar to what US individualist anarchists such as Josiah Warren, William B. Greene, and Benjamin Tucker proposed. Mainly a non-capitalist market economy composed of self employers-both individuals and worker´s cooperatives. all of these 19th century authors have long works focused on the issue of economics to the point of being able to be judged as "economists" or ·"economicistic" authors. The best and most extensive recent economist of this point of view is clearly Kevin Carson and his Center for a Stateless Society. He has written many books on this subject such as "Studies of mutualist political economy" and "organizational Theory" which are very deep works as far as economics go and which have updated the views of Tucker and Proudhon taking into account recent developments both in economic theory and historical events.
Anarchist work on economics outside the academic discipline of economics:
After political, academic and economic developments of the 1960s nad 1970s, there emerged a criticism of the academic discipline of economics from fields such as sociology (economic sociology), antropology (economic antropology), history (economic history) and cultural studies. As such that ended up expressing from anarchist points of view in the most developed, extensive and dedicated form in the work of David Graeber and works like "Debt: the first 4000 years" and his most recent "The Utopia of Rules: On Technology, Stupidity, and the Secret Joys of Bureaucracy" among other works. Graeber is already a big name within the sub-field of "economic antrhopology" and is also read and commented in "economic sociology". Reading him is a good antidote to the economicism that can be present in an author such as Kevin Carson or in the excessive reliance on a "model" present in Michael Albert.
Participatory Economics is a kind of democratic decision making about production, consumption, and work. It values self-management, equity, diversity, and solidarity. It aims to promote those values through council decision making, balanced jobs, and reward (pay) for effort and sacrifice.
The authors of Parecon are profs. Michael Albert and Robin Hahnel.
http://zcomm.org/looking-forward/ Looking Forward is a good primer.
Edit: removing whiny self-indulgence.
The main objection to Parecon appears to be that it uses accounts of earned consumption rights, rather than a direct transmission of goods.
Full answers to all that would take thousands of words - and they do, in the free book linked above, as well as Parecon: Life After Capitalism and Of The People, By The People: The Case for a Participatory Economy, as well as discussions on zcomm.org.
"Who creates money" can mean several things. If you mean "who mints coins and prints bills", maybe no one. Electronic exchange is probably good enough to supplant physical tender. If you mean "who causes a store of value to be recorded," then the (simplified) answer is "co-equal councils of workers whose balanced job complexes encompass crediting workers for the agreed value of their work." In short, bookkeepers. If you mean "who establishes relative value", the answer is basically "everyone".
Full, satisfying answers are available, but writing them in a comment here is impractical. If the free book above is too much to start with, try this discussion: https://zcomm.org/znetarticle/of-the-people-by-the-people-by-robin-hahnel/
There are many more discussions on zcomm also. Look around, I'm sure you'll find stimulating ideas. :-)
"If you mean "who mints coins and prints bills", maybe no one. Electronic exchange is probably good enough to supplant physical tender..."
no one mints or prints today either. electronic exchange has already supplanted physical tender (to the tune of around 99% of "money").
as long as accounting and crediting happens, you don't have much fundamental difference than what we have today.
when I think of an alternative to our present money system, I think of things I can do right now, today, that work fundamentally differently - and for that reason i desire to live as much as possible with a gift mentality.
I disagree. A system that eliminates profit, prioritizes meeting people's needs, respects ecology, and promotes human solidarity is very different from a system that deifies profit, prioritizes expanding consumption, destroys ecology, and promotes emotional isolation. Even if they both use numbers to keep track of how much we have produced and consumed.
i should probably have said ' not different enough in the ways that i desire."