Enthalpy definitions. What are their main differences?
Explanation of notation:
$H$ is the enthalpy of the system.
$\Delta$ means change of, so $\Delta H$ means change of the enthalpy

This symbol means standard condition, standard condition is defined as a pressure of $100\text{kPa}$ and reactants and products are in their standard state, or concentration of solutions are $1\text{M}$. However, since LaTeX doesn't have this symbol, I'll substitute it for $^\ominus$.
Enthalpy changes:
Enthalpy of dilution – The enthalpy change when a solution containing one mole of a solute is diluted from one concentration to another.
Enthalpy of ($n\text{th}$) electron affinity – The enthalpy change when $n$ electrons are added to one mole of gaseous atoms.
$$\ce{Li(g) + e-(g) -&gt; Li-(g) +60\ \text{kJ}}$$
$$\ce{F(g) + e-(g) -&gt;  F-(g) +328\ \text{kJ}}$$
Enthalpy of ($n\text{th}$) ionization – The enthalpy change when $n$ electrons are removed from one mole of gaseous atoms. It is always positive.
$$\ce{Li(g) +520\ \text{kJ} -&gt; Li+(g) +e-(g)}$$
$$\ce{He(g) +2372\ \text{kJ} -&gt; He+(g) +e-(g)}$$
Enthalpy of lattice dissociation – The enthalpy change when one mole of an ionic lattice dissociates into isolated gaseous ions.
An example for sodium chloride which have an enthalpy of lattice dissociation, also known as lattice energy, of $787\ \mathrm{kJ/mol}$
$$\ce{NaCl(s) +787\ \text{kJ} -&gt; Na+(g) + Cl-(g)}\qquad\Delta H=787\ \text{kJ/mol}$$
Enthalpy of lattice formation – The enthalpy change when one mole of solid crystal is formed from its scattered gaseous ions.
$$\ce{Na+(g) + Cl-(g) -&gt; NaCl(s)} +787\ \text{kJ}\qquad\Delta H=-787\ \text{kJ/mol}$$
Which means Enthalpy of lattice dissociation$=-$Enthalpy of lattice formation
Enthalpy of hydration($\Delta_\text{hyd}H^\ominus$) – Enthalpy change when when one mole of ions undergo hydration.
Enthalpy of mixing – The enthalpy change from a substance when mixed.
Enthalpy of neutralisation – The enthalpy change when an acid is completely neutralised by a base.
For a strong acid, like $\ce{HCl}$ and strong base, like $\ce{NaOH}$, they disassociate almost completely $\ce{Cl-}$ and $\ce{Na+}$ are spectator ions so what is actually happening is $$\ce{H+(aq) + OH-(aq) -&gt; H2O(l) + 58\ \text{kJ/mol}}$$
However, using a weak acid/base will have a lower enthalpy of neutralisation as normally most of the acid/base does not disassociate.
For example, mixing ethanoic acid and potassium hydroxide only has a enthalpy of neutralisation of $-11.7\ \text{kJ/mol}$
Enthalpy of precipitation – The enthalpy change when one mole of a sparingly soluble substance precipitates by mixing dilute solutions of suitable electrolytes.
Enthalpy of solution – Enthalpy change when 1 mole of an ionic substance dissolves in water to give a solution of infinite dilution.
Enthalpy of solution can be positive or negative as when a ionic substance dissolves, the dissolution can be broken into three steps

Breaking of solute-solute attraction (endothermic)
Breaking solvent-solvent attraction (endothermic), eg. hydrogen bonds, LDF
Forming solvent-solute attraction (exothermic)

An example of a positive enthalpy of solution is potassium chlorate which has an enthalpy of solution of $41.38\ \text{kJ/mol}$
Enthalpy of (Solid$\rightarrow$Liquid: $\Delta_\text{fus}H^\ominus$, Liquid$\rightarrow$Solid:$\Delta_\text{freezing}H^\ominus$, Liquid$\rightarrow$Gas: $\Delta_\text{vap}H^\ominus$, Gas$\rightarrow$Liquid: $\Delta_\text{cond}H^\ominus$, Solid$\rightarrow$Gas: $\Delta_\text{sub}H^\ominus$, Gas$\rightarrow$Solid: $\Delta_\text{deposition}H^\ominus$) – The enthalpy change from providing energy, to a specific quantity of the substance to change its state.
$$\Delta_\text{fus}H^\ominus=-\Delta_\text{freezing}H^\ominus,\Delta_\text{vap}H^\ominus=-\Delta_\text{cond}H^\ominus,\Delta_\text{sub}H^\ominus=-\Delta_\text{deposition}H^\ominus$$
Standard enthalpy of atomization($\Delta_\text{at}H_T^\ominus$) – Change when a compound's bonds are broken and the component atoms are reduced to individual atoms at at $T^\circ K$.
$$\ce{S_8 -&gt; 8S}\qquad\Delta_{at}H^\ominus=278.7\ \text{kJ/mol}$$
Standard enthalpy of combustion($\Delta_\text{c}H_T^\ominus$) – The enthalpy change which occurs when one mole of the compound is burned completely in oxygen at $T^\circ K$ and $10\ \mathrm{kPa}$.
$$\ce{H2(g) +\frac{1}{2}O2(g) -&gt; H2O(g)}+572\ \text{kJ}\qquad\Delta_cH^\ominus = -286\ \text{kJ/mol}$$
Standard enthalpy of formation($\Delta_\text{f}H_T^\ominus$) – Change in enthalpy during the formation of one mole of the compound from its constituent elements, with all substances in their standard states, and at a pressure of $100\ \mathrm{kPa}$ at $T^\circ K$.
It can be calculated using Hess's law if the reaction is hypothetical. An example is methane, $\ce{C}$ and $\ce{H2}$ will not normally react but the standard enthalpy of formation of methane is determined by Hess's law to be $-74.8\ \text{kJ/mol}$
$$\ce{\frac{1}{2}N2(g) +\frac{1}{2}O2(g) -&gt; NO(g)}\qquad\Delta_\text{f}H^\ominus=90.25\ \text{kJ/mol}$$
Standard enthalpy of reaction($\Delta_\text{r}H^\ominus_T$) – Enthalpy change that when matter is transformed by a chemical reaction at $T^\circ K$ and $10\ \mathrm{kPa}$.
$$\ce{H2(g) +\frac{1}{2}O2(g) -&gt; H2O(g)} +572\ \text{kJ}\qquad\Delta_\text{r}H^\ominus = −572\ \text{kJ/mol}$$
$$\Delta_\text{r}H^\ominus=\sum H^\ominus_\text{products}-\sum H^\ominus_\text{reactants}$$
$$\Delta_\text{r}H_\text{forward}=-\Delta_\text{r}H_\text{backwards}$$
Laws:
Le Chatelier's Principle – When an external change is made to a system in dynamic equilibrium, the system responds to minimise the effect of the change.
Yellow $\ce{Fe^3+}$ reacting with colorless thiocyanate ions $\ce{SCN-}$ to form deep red $\ce{[Fe(SCN)]^2+}$ ions:
$$\ce{Fe^3+(aq) + SCN-(aq) -&gt; [Fe(SCN)]^2+(aq)}$$
When $\ce{NH4Cl}$ is added, $\ce{Cl-}$ reacts with $\ce{Fe^3+}$ ions to form $\ce{[FeCl4]-}$ ions. By the Le Chatelier's Principle, when $\ce{Cl-}$ is added into a solution of deep red $\ce{[Fe(SCN)]^2+(aq)}$ ions, the equilibrium will shift to $\ce{Fe^3+(aq) + SCN-(aq)}$, turning the solution pale red.
Kirchhoff's Law – Enthalpy of any substance increases with temperature.
Hess's Law – Total enthalpy change of a chemical reaction is independent of the number of steps the reaction takes.
Henry's Law – Amount of dissolved gas is proportional to its partial pressure in the gas phase.
Processes:
Constant Entropy – Isoentropic
Constant Pressure – Isobaric
Constant Volume – Isovolumetric
Side note: This is probably not a complete list as I may have missed some