Which is the best way to insert a list inside a cell in SQL?

I am creating a simple social network in which I use xampp (and so, mysql and php).
I am facing a dilemma regarding which is the best way to include a list of objects as an element of a row.

I'll explain it better: in my project, which contains students and professors as unique users, every one of them has a list of projects they are partecipating into, and every project has a list of industries/firms/companies who are financing or simply observing the project; every company has its own profile.

My dilemma regards which is the best way to represent this architecture:

• should I create a table for every project, in which there's only one column listing all the companies?
  
• should I create a reference table that contains in every row the code of a single project, and as many columns as the number of companies related to it (I don't know if sql allows an arbitrary, auto-incrementable number of columns)?
  
• should I create a table with all the projects datas and add a column in the end in which I'll compress all the codes of the companies?
  
• other I can't figure out right now?
  
  The tricky part for me is that I need to do something similar four or five times in all the project (not only for the companies), with the risk of creating a lot of tables (and a lot of confusion), but at the same time with a lot of complexity parsing the lists if I compress them in one cell only...
  Any suggestion?

What you are asking about, without knowing, is the concept of normalization. It's worth looking into. A simple design for your system could look like this:

people(id, name, ... type)
projects(id, name, ... )
people_projects(project_id, people_id)
companies(id, name, ...)
company_projects(company_id, project_id)

Each professor or student is a single row in the people table. Each project is a single row in the projects table, each person ON a project, is a single row in the people_projects table. same for companies.

You then access your information via joining the tables together, eg to get all students on the project with name 'Project X', you would do a simple inner join:

select *
  from projects p
    inner join project_people pp
      on p.id = pp.project_id
    inner join people pl
      on pp.people_id = pl.id
  where p.name = 'Project X'
    and pl.type = 'student';

Simple, robust database schema, and simple data access.