Some books on Likelihood Estimation
* Amari, Barndorff-Nielsen, Kass, Lauritzen and Rao, Differential geometry in statistical inference. $-\small{\text{Geometrical approach for proving existence, uniqueness and other properties of MLE.}}$
* Buttler, Saddlepoint Approximations with Applications.
$-\small{\text{Saddlepoint approximations to the MLE on complicated models.}}$* Cox, Principles of Statistical Inference.
$-\small{\text{A basic reference on MLE.}}$* Cox and Barndorff-Nielsen, Inference and Asymptotics. $-\small{\text{Likelihood, pseudo-likelihood, approximation theorems and asymptotics explained by}}$ $ \small{\text{two exponents in this area.}}$
* Edwards, Likelihood.
$-\small{\text{A reference for a general discussion on this concept.}}$* Ferguson, A Course in Large Sample Theory. $-\small{\text{Contains classical results on asymptotic properties of point estimators.}}$
* Kalbfleisch, Probability and Statistical Inference II.
$-\small{\text{Introductory book containing interesting basic results such as the continuous }}$ $\small{\text{approximation to the likelihood which is not always explained.}}$* Lehmann and Cassella, Theory of Point Estimation.
$-\small{\text{Classical results on point estimation, an essential reference.}}$* Pace and Salvan, Principles of Statistical Inference: From a Neo-Fisherian Perspective. $-\small{\text{A good reference on a school of thought becoming more and more popular:}}$ $\small{\text{the Neo-Fisherian.}}$
* Pawittan, In All Likelihood: Statistical Modelling and Inference Using Likelihood.
* Serfling, Approximation Theorems of Mathematical Statistics. $-\small{\text{More rigourous book, here you can find the mystical "regularity conditions".}}$
* Severini, Likelihood Methods in Statistics.
* Shao, Mathematical Statistics.
$-\small{\text{Classical results, good as a textbook.}}$* Sprott, Statistical Inference in Science. $-\small{\text{Basic reference on likelihood, profile likelihood and classical statistical modelling.}}$
* van der Vaart, Asymptotic Statistics.
$-\small{\text{A general reference on: modes of convergence, properties of MLE, delta method,}}$ $\small{\text{ moment estimators, efficiency and tests.}}$* Young and Smith, Essentials of Statistical Inference. $-\small{\text{A more recent book on: Likelihood, pseudolikelihood, saddlepoint approximations,}}$ $\small{p^*\text{ formula, modified profile likelihoods and more.}}$