Source of information on the evolution of aging/senescence
I don't know about just one source that fits everything you've asked, so here's a custom bibliography to get you started instead.

General Sources

I first learned about biogerontology from the excellent series of introductory essays at João Pedro de Magalhães' website, senescence.info; I definitely recommend starting here. 

A short book written by two experts, for Scientific American Publishers, is Finch and Ricklefs' Aging: A Natural History. "The" book on the Evolutionary Theory of Aging is Michael Rose's Evolutionary Biology of Aging. "The" book on comparative biogerontology is Finch's Longevity, Senescence, and the Genome. A "pop" account of recent research (esp. to do with caloric restriction and long-lived mutants, which have people excited right now, and the search for longevity drugs) is David Stipp's The Youth Pill. A constantly-updated-with-new-editions-reference is The Handbook of the Biology of Aging. In 2008 (just missing the 2009 rapamycin excitement), Cold Spring Harbor Press published a collection on Molecular Biology of Aging. The Gerontological Society of America has an e-textbook out, that I think is going to be updated on the regular, called Molecular and Cellular Biology of Aging.

The Definition and Measurement of Aging

Usually, people define senescence as an increase in "mortality" with age. Mortality roughly means vulnerability; the older you are, the easier it is to die. Mortality is measured/estimated demographically, in terms of (hypothetical or actual) cohort survivorship. There are two quantities usually used: one for discrete-time, and one for continuous-time. Where $N_x$ the number of survivors still alive in a cohort at age $x$,

$q_x = \frac{{N_x}-{N_{x+1}}}{N_x}$ discrete-time; The Age-Specific Probability of Death.

$\mu_x = -\frac{N^{'}_{x}}{N_x}$ instantaneous; The Force of Mortality.

The first one is the fraction, of those alive at age $x$, who will die before age $x+1$. This estimates the probability that an individual aged $x$ will die before age $x+1$. This is intuitive: to age means that an 80-year-old is less likely to make it to 81, than a 20-year-old is to make it to 21. Notice that $q_x$ is bounded between 0 and 1. 

The second one is the instantaneous rate of death, normalized against cohort size at that instant (whereas the first was the number of deaths in an interval, normalized against cohort size at the beginning of the interval). It is the instantaneous, age-specific, per-capita death rate. It can be visualized as the slope of the survivorship curve, divided by its height, times -1 to make it positive. It is not a probability. It has a dimension of rate ("per-second", "per-hour", etc) and it has no upper bound.

This way of defining senescence is described in Nature Scitable's Aging and its Demographic Measurement (although the authors give an erroneous definition of the force of mortality). It is discussed and justified intuitively, and at length, in Peter Medawar's The Definition and Measurement of Senescence.

Sometimes, you might want to count a decline in fecundity as aging, too, even if mortality wasn't changing. Or, you might want to define senescence in terms of various kinds of physiological performance. This is really a matter of taste, I suppose, or of what kinds of question you're trying to answer. Ageing or Senescence is just the part of getting older which, on top of having more birthdays, is somehow or other "bad" for you.

But the most common criterion is that $q_x$ or $\mu_x$ grows with age.

Mainstream Evolutionary Theory of Aging:

The mainstream idea is that aging evolves because of the declining force of natural selection with age. Natural selection "cares less" about things that happen late in life, than about things that happen early in life.


Mutation Accumulation (MA): the theory proposed in Peter Medawar's An Unsolved Problem of Biology. (Theory that aging is due to genes that are silent or neutral in early life, and deleterious in late life.)
Antagonistic Pleiotropy (AP): the theory proposed in George C. Williams' Pleiotropy, Natural Selection, and the Evolution of Senescence. (Theory that aging is due to genes that are beneficial in early life, and deleterious late in life.)
Disposable Soma: Proposed by Thomas Kirkwood and Robin Holliday; sometimes considered a version of AP. (Theory that aging is due to a tradeoff, in turn possibly due to allocation of limited resources, between reproduction and maintenance; selection favours less than perfect maintenance. Can be considered a version of AP where the "early beneficial effect" is increased maintenance, and the "late deleterious effect" is decreased survival.)


Summarized in Nature Scitable's The Evolution of Aging. Note that both MA and AP could be partly true; both kinds of genes could exist.

Both MA and AP are commonly cited as predicting that higher extrinsic mortality should lead to the evolution of earlier / faster senescence; but things may be more complicated than this.

The Declining Force of Natural Selection: Hamilton's Formalization

Medawar's and Williams' insights were verbal. William Hamilton did the math, and showed that certain formal indicators of the strength of selection on a genetic effect, necessarily declined with the age at which that effect occurs. These indicators were I think: 1) the partial derivative of $r$ (the intrinsic rate of increase / malthusian parameter, which he took to be fitness) with respect to the force of mortality at age $x$; and 2) the partial derivative of $r$ with respect to fecundity at age $x$. (The first starts declining at the age of first reproduction; the second starts declining immediately.)

In passing, this also demonstrated that a remark R. A. Fisher had previously made, and which Medawar had accepted, was fallacious. Fisher and Medawar had assumed that the strength of natural selection was proportional to age-specific reproductive value; but since reproductive value can increase with age, and Hamilton's indicators can't, reproductive value can't be measuring the sensitivity of $r$.


Hamilton's paper: The Moulding of Senescence by Natural Selection.
Charlesworth summarizes Hamilton's results and puts them in context in Fisher, Medawar, Hamilton and the Evolution of Aging.
Charlesworth's book Evolution in Age-Structured Populations is supposed to be quite important and to have furthered and refined stuff in this area.
Apparently things might be a bit more complicated than this? Baudisch has claimed that although Hamilton's indicators must decrease with age, other indicators, which aren't obviously unreasonable, can increase.


Gompertz, Weibull, and Gompertz-Makeham

The Gompertz equation is intended to describe how the Force of Mortality $\mu_x$ grows with age. The Gompertz equation was come up with empirically, not for any theoretical reason; it just seemed to Benjamin Gompertz to fit the data quite well, for a good stretch of adult lifespan. The same goes for the Weibull equation, as far as I know, and for the Gompertz-Makeham equation.


Gompertz is an exponential growth equation: $\mu_x = \mu_0 \cdot e^{Gx}$ (where $G$ is a parameter). It looks like a straight line when graphed on a semilog plot.
Weibull is a power growth equation: $\mu_x = A \cdot x^B$ (where $A$ and $B$ are parameters). It looks like a straight line when graphed on a log-log plot.
Gompertz-Makeham adds a constant to the Gompertz equation: $\mu_x = \mu_0 \cdot e^{Gx}+C$. This ruins the elegance of the semilog-graphing, alas; it doesn't look like a straight line.


Apparently some people have tried to show how eg. Gompertz can evolve in MA models, but the generality of this is questionable (see Box 2 in this Trends in Ecology and Evolution paper). Gavrilov and Gavrilova (proponents of the "reliability theory of aging", have said something about Gompertz and Weibull being special: ("Both the Gompertz and the Weibull failure laws have their fundamental explanation rooted in reliability theory... and are the only two theoretically possible limiting extreme value distributions for systems whose life spans are determined by the first failed component... In other words, as the system becomes more and more complex (contains more vital components, each being critical for survival), its life span distribution may asymptotically approach one of the only two theoretically possible limiting distributions—either Gompertz or Weibull (depending on the early kinetics of failure of system components).") I don't know what that means.

Gompertz is the most commonly cited / used equation, I think. It's supposed to be more accurate than Weibull. Gompertz-Makeham I guess is more accurate, but of course it would be - it has an extra adjustible parameter, which, if it isn't helping, you can just set to zero!

Sometimes these equations are erroneously presented in terms of $q_x$ instead of $\mu_x$. This is erroneous historically, but also because $q_x$ has an upper bound of 1 and couldn't possibly obey any of the equations, at least not indefinitely.

Sometimes people find it more intuitive to describe Gompertz' exponential growth in terms of how long it takes $\mu_x$ to double; in humans, this "Mortality Rate Doubling Time" is about eight years.

Note that the equation does not accurately describe early life; mortality often starts high in infants, before falling to its minimum, and then starting to grow again. Thus $\mu_0$ isn't the actual mortality rate at age 0, but the backwards-extrapolated mortality rate you would have had at age 0, if you were perfectly Gompertzian (or whatever).

It also may not describe very late life. A hot topic right now is "late-life mortality deceleration", where the exponential growth seems to slow down such that Gompertz overpredicts mortality in the very old; whether this is so, and why, is debated.

Reliability Theory and the Reliability Theory of Aging

"Reliability Theory" itself is just a mathematical framework for describing survival / failure rates and stuff. (Engineers use it to quantify stuff like, the rate at which parts have their first breakage, or whatever.) Some of the quantities it describes are basically the same as some analogous quantities in demography / life histories, if "first failure" is taken to mean death. For example, the "Survival Function" $S(t)$ is the probability, at time $0$, that failure will not yet have occurred by time $t$; this is obviously analogous to the probability $l_x$ that a newborn will still be alive at age $x$.

Systems can be made of parts; if you know the survival/reliability patterns of the parts, and how they go together, you can tell something about the survival/reliability of the whole system. To illustrate, compare two kinds of reliability structure:


A "series reliability structure" is one where, if any part fails, the system fails. An example would be a block held up by a chain; if any link breaks the block falls.
A "parallel reliability structure" is one where, if all parts fail, the system fails. An example would be a block held up by a number of individual rings, attached separately; only when the last ring breaks, does the block fall.


"The Reliability Theory of Aging and Longevity" is a specific theory proposed by Leonid Gavrilov and Natalia Gavrilova, intended to explain patterns of organismal failure ("death") in terms of component failure, and how the components are put together. If I recall, they propose that aging organisms are made up of redundant blocks of non-aging components; supposedly, this can explain near-Gompertzian aging over most of adult life, as well as apparent late-life mortality deceleration.

Group Selection

Heresy! Most evolutionary biologists / gerontologists, I assume, are happy with the mainstream theory and don't take the group selection theory seriously. Iunno, try Mitteldorf? Here's a paper and he also wrote a pop book with Dorion Sagan. On group selection in general as an explanation for altruism, I think David Sloan Wilson's the guy trying the hardest to defend it (or "a new version of it").

Molecular Mechanisms

Iunno, try The Hallmarks of Aging? The trouble is we really don't know what mechanisms cause aging. There's some good ideas, but finding evidence is haaaaard. One problem is that, if you want to know why some species live longer than others, and you're looking for physiological correlations, body size is a huge confound (elephants and whales live longer than mice and dogs), and so might be phylogeny.