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Introduction Notations and conventions $\mathcal R$-Boundedness and Sectorial Operators: Sectorial operators The classes ${\mathcal{BIP}}(X)$ and $\mathcal H^\infty(X)$ $\mathcal R$-bounded families of operators $\mathcal R$-sectorial operators and maximal $L_p$-regularity Elliptic and Parabolic Boundary Value Problems: Elliptic differential operators in $L_p(\mathbb{R}^n;E)$ Elliptic problems in a half space: General Banach spaces Elliptic problems in a half space: Banach spaces of class $\mathcal{HT}$ Elliptic and parabolic problems in domains Notes References.