Here is Diamond's home page, here is Diamond on Wikipedia.  Diamond has been at MIT since 1970 and he is considered one of the bulwarks there, having produced many excellent students, including Bernanke and Andrei Shleifer.  Here is the bit of most current interest:

On April 29, 2010, Diamond was announced by Barack Obama as one of three nominees to fill the three vacancies then present on the Federal Reserve Board, along with Janet Yellen and Sarah Bloom Raskin.^[5] On August 5 the Senate returned Diamond's nomination to the White House, effectively rejecting his nomination. Ben Bernanke, the current Chairman of the Fed, was once a student of Diamond.

Some of Diamond's early work was in capital theory, as he outlined the conditions under which, in dynamic growth models, the level of capital could be inefficient.  Read this paper, from 1965, which is still his most frequently cited work.  It helped produce a standard framework for thinking about national debt and economic growth.

Diamond has contributed plenty to the theory of optimal taxation, in particular when linear commodity taxes are optimal and how to use the tax system for redistribution.  See this paper with James Mirrlees (also a Nobel Laureate) and also this one.  One implication is that taxing inputs often leads to more distortion than taxing outputs and you can think of this as one possible motivation for a consumption tax.

Here is Diamond's 1982 paper on macro and search theory, which I think of as his most influential.  The abstract is classic Diamond:

Equilibrium is analyzed by a simple barter model with identical risk-neutral agents where trade is coordinated by a stochastic matching process.  It is shown that there are multiple rational expectations equilibria, with all non-corner solution equilibria inefficient.  This implies that an economy with this type of trade friction does not have a unique rate of natural unemployment.

The relationship to the current day U.S. is striking.  One point he stresses is that subsidization of production can make sense and also that there can be real costs of converging to the lowest possible rate of unemployment too quickly.  This remains an important "framework" paper for analyzing the interaction of search and aggregate demand.  His other 1982 search paper implies that labor mobility will be less than is socially optimal.  This paper on search theory shows that unemployment compensation can lead to better job matches, by limiting crowding externalities in the job market.

He and Olivier Blanchard wrote a classic piece on the Beveridge Curve, which is about the relationship between job vacacies and the unemployment rate.  Some commentators cite the Beveridge Curve as evidence for structural unemployment, although this is controversial.

Diamond has written a great deal on social security, often at the applied level.  Here is his paper criticizing social security privatization in Chile for its high costs.  Here is his survey on social security reform proposals.  Here is his paper on macro and social security reform.  Here is a very good European talk he gave on pension issues.  Diamond wrote a book with Peter Orszag on social security and he has been a major influence on Democratic Party thinking on this issue; the book looks closely at progressive price indexing rather than wage indexing of benefits.  Here is a CBO summary and analysis of the plan.  Much of Diamond's more formal social security analysis stresses risk-sharing issues and in general he often points out that social security proposals, including Bush's privatization idea, are not well-grounded in rigorous analysis.

Here Diamond tells us not to expect 7 percent stock returns for the ongoing future.

Diamond has many interests, here is his survey on contingent valuation and whether some number is better to use than no number at all.  He and Stiglitz wrote a famous paper on risk and risk aversion.

Personally, my favorite Diamond paper is this short gem on the evaluation of infiinite utlity streams; it will make your head spin, as it asks whether we have coherent means of thinking about prospects with infinite utility and in general how intertemporal utility streams should be ordered.  See also his related paper on stationary utility, co-authored with T.J. Koopmans.

Here is his short introduction on behavioral economics.

I think of Diamond as the classic MIT economist, especially of the earlier, pre-Acemoglu generation.  Lots of theoretical rigor, though sometimes his theory pieces don't have a simple or simply analytic punchline.  There is greater concern with risk, and stability conditions, and dynamic and border conditions, than you would see in a Chicago theory paper.  There is a strong emphasis on the ability of government to implement welfare-improving schemes of the sort found in social democracies.  The approach is quite technocratic — solve and advise.  Public choice and political economy considerations take a back seat.  High IQ.  Of the MIT economists, he has done the most to pursue the Samuelson tradition of having a universal method and very broad interests.  His papers remain central to public finance, welfare economic, intertemporal choice, search theory, macroeconomics, and other areas.  His policy impact on social security has been significant.

Addendum: Levitt comments on Diamond.

Without any taxes, accepting that editor’s assignment would have yielded my children an extra $10,000. With taxes, it yields only $1,000. In effect, once the entire tax system is taken into account, my family’s marginal tax rate is about 90 percent. Is it any wonder that I turn down most of the money-making opportunities I am offered?

By contrast, without the tax increases advocated by the Obama administration, the numbers would look quite different. I would face a lower income tax rate, a lower Medicare tax rate, and no deduction phaseout or estate tax. Taking that writing assignment would yield my kids about $2,000. I would have twice the incentive to keep working.

The full column is here.  Perhaps Greg could do more to (legally) evade the estate tax, but that's hardly an argument for raising such a tax.

Alternatively, Dan Ariely asks:

Let’s say that your 1040 came with a little extra stuff: maybe a container with an alcohol content, or perchance something of the chocolate persuasion. What if your tax forms arrived in a gift box with some financial documents on the side? What if the instructions for filling out the form told you to type in your personal information and take a bite of chocolate, type in your W-2 information and drink some of the alcohol, add your deductions and try some of the nuts etc? What if we could live in a world where you actually looked forward filling out these forms?