There has always been a place in biology for words that have different meanings for different people. Epigenetics is an extreme case, because it has several meanings with independent roots. (Bird 2007)

The meaning of the term "epigenetics" has itself undergone an evolution. (Felsenfeld 2014)

the causal study of embryological development (Waddington 1957, The strategy of the genes)

The study of mitotically and/or meiotically heritable changes in gene function that cannot be explained by changes in DNA sequence
(Riggs et al. 1996)

a change in the state of expression of a gene that does not involve a mutation, but that is nevertheless inherited in the absence of the signal (or event) that initiated the change. (Ptashne and Gant 2002)

the structural adaptation of chromosomal regions so as to register, signal or perpetuate altered activity states. (Bird 2007)

the causal study of embryological development (Waddington 1957, The strategy of the genes)

The study of mitotically and/or meiotically heritable changes in gene function that cannot be explained by changes in DNA sequence
(Riggs et al. 1996)

a change in the state of expression of a gene that does not involve a mutation, but that is nevertheless inherited in the absence of the signal (or event) that initiated the change. (Ptashne and Gant 2002)

the structural adaptation of chromosomal regions so as to register, signal or perpetuate altered activity states. (Bird 2007)

Epigenetics refers to changes in gene regulation brought about through modifications to the DNA's packaging proteins or the DNA molecules themselves without changing the underlying sequence.
(Lord and Cruchaga 2014, Nature Neuroscience)

the study of the mechanisms that allow cells to translate the nearly constant genome content of a multicellular organism into multiple functional and stable cellular conditions (Schwartzman and Tanay 2015)

Epigenetic processes are a means by which endogenous and exoge­nous cues exert long-term control over gene expression (Nugent et al. 2015)

The word literally means "on top of genetics," and it's the study of how individual genes can be activated or deactivated by life experiences. (The Week, 2013)

epigenomics is the study of the physical modifications, associations and conformations of genomic DNA sequences (Schwartzman and Tanay 2015)

epigenomics is the study of the chemical modification and physical conformation of cellular DNA and bound proteins (Sheffield 2017)