Considering this is an Economics Stack Exchange site, I’m going to answer in the spectre of Financial Economics. These are the most foundational equations and ideas of Financial Economics to understand more complex applied or academic research.
1. Gross yield
The gross yield is the yield on an investment before the deduction of taxes and expenses.
$$1+R_{t+1}=\frac{P_{t+1}+D_{t+1}}{P_t}$$
$R_{t+1}$: net yield
$P_{t+1}$: price of the financial asset
$D_{t+1}$: dividend
2. Present Value
Present value ($PV$) is the current worth of a future sum of money or stream of cash flows given a specified rate of return.
$$PV=\frac{FV_n}{(1+R)^n}$$
$FV$: future value $R$: interest rate
3. Gordon’s growth model
The Gordon growth model is used to determine the intrinsic value ($V_0$) of a stock based on a future series of dividends ($D_0$) that grow at a constant rate ($g$).
$$V_0=D_0 \frac{1+g}{R-g}$$
$R$: interest rate
4. Bond pricing
The price of a bond is the sum of the present values of all expected coupon payments plus the present value of the par value at maturity.
$$P_{bond}= \sum_{t=1}^T \frac{\text{Interest}}{(1+r_{it})^2}+\frac{\text{Par Value}}{(1+r_{iT})^2}$$
5. Duration
A measure of the sensitivity of the price (the value of principal) of a fixed-income investment to a change in interest rates. Given the relation between present value, future cash-flow and yield to maturity:$$PV=\frac{\sum CF_t}{(1+YTM)^t}$$
The second order Taylor polynomial is the following:
$$dPV=\underbrace{
\left(
\frac{dPV}{dYTM}
\right)dYTM}_{\textbf{Duration}}+
\underbrace{\left(
\frac{1}{2}
\right)
\left(
\frac{d^2 PV}{dYTM^2}
\right)dYTM^2}_{\text{Convexity}}$$
$YTM$: yield to maturity
6. Convexity
For any given bond, a graph of the relationship between price and yield is convex. This means that the graph forms a curve rather than a straight-line (linear). The degree to which the graph is curved shows how much a bond's yield changes in response to a change in price.
$$dPV=\underbrace{
\left(
\frac{dPV}{dYTM}
\right)dYTM}_{\text{Duration}}+
\underbrace{\left(
\frac{1}{2}
\right)
\left(
\frac{d^2 PV}{dYTM^2}
\right)dYTM^2}_{\textbf{Convexity}}$$
7. Liquidity premium
A premium that investors will demand when any given security cannot be easily converted into cash, and converted at the fair market value.
8. CAPM (Capital Asset Pricing Model)
A model that describes the relationship between risk and expected return and that is used in the pricing of risky securities. It can be estimated by simple OLS:
$$ER_i=R_f + \beta_i(ER_m-R_f)$$
$ER_i$: expected return of portfolio $i$, $ER_m$: expected return of the market portfolio, $R_f$: risk-free portfolio, $\beta_i$:CAPM-beta of portfolio $i$
