This is a huge topic. I would recommend the careful reading of a textbook like

Diggle, P. J.; Heagerty, P.; Liang, K.-Y. & Zeger, S. (2002). Analysis of longitudinal data. Oxford University Press, 379 p.

which I found quite illuminating.

Thanks for your answer and recommendation, I will.

A change score is generally not recommended as a change of 10 when the past score is a thousand is not the same as a change of 10 when the past score is 10.

If you have two time points I would regress current Y on past Y as then you are modeling change rather than Ycurrent minus Y past as the response variable.

If you have more than two time points then you have longitudinal or panel data which is characterized by dependent data and time varying and time invariant predictors.  .

There is a sizeable debate over the appropriateness of fixed effects ( you put in dummies for each occasion ) and a random coefficients approach which models between individuals and within individual between occasions differences  I prefer the latter due to its  flexibility - and make the argument here

https://www.researchgate.net/publication/233756428_Explaining_Fixed_Effects_Random_Effects_Modeling_of_Time-Series_Cross-Sectional_and_Panel_Data

There are lots of free resources at this site on the random effects multilevel approach

http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#multipleresp

Article Explaining Fixed Effects: Random Effects Modeling of Time-Se...

Thank you very much, your answer and the paper were really helpfull.

Hi, I agree with Marek that Singer & Willet is a very good textbook about technical issuesof longitudinal analysis.  You may find some generic although useful ideas in my PhD thesis (although full text in spanish, below it share link to academia.edu). I summarize some ideas:

In their academic and professional practices social scientists were usually focused on the study of their contemporary societies, and in the analysis of cross-sectional data. Today, we find a renewed attention on the empirical analysis of the processes of change using diachronic data analysis (Singer & Willet, 2003), and in the development of long term longitudinal research programs, mainly in Europe and United States. This renewed interest in time from a theoretical and methodological point of view, surely enriches the social sciences, and helps to address the long- term consequences of social actions.

"The study of change raises a necessary review of the theoretical, epistemological and methodological assumptions involved. Some of these problems require an interdisciplinary approach of issues as irreversibility (Prigogine, 1993; Prigogine, Stengers, 1984), probability of events, and ordering of causes and effects in time. Four methodological and epistemological challenges for the analysis of time are identified: 1) the presence of irreversible effects - which occur in one direction in time -- , with a disruption of the symmetry between “ before” and “after” (Prigogine, 1993), in some variables as formal education, if you have secondary level degree, you will never go back to primary; 2) obsolescence of indicators that operationalize concepts: in social sciences the relationship between the concept and the indicator may not be constant over time (Oliva, 2014); 3) the difficulties of forecasting and prognosis of variables in social structures and scenarios; 4) the distinction between cause and effect, considering an temporary sequence where the cause (or independent variable) is previous to the effect (or dependent variable, respectively)".

https://www.academia.edu/19868954/Desaf%C3%ADos_del_an%C3%A1lisis_del_tiempo_en_las_ciencias_sociales

Also:

http://es.slideshare.net/IleanaFarre/ppt-seminario-miguel-olivaversionfinal

Good luck!!!

Miguel